Find Volume With Fractional Edge Lengths - 6th Grade Math

A rectangular prism is filled by packing $\tfrac{1}{2}\text{ ft} \times \tfrac{1}{2}\text{ ft} \times \tfrac{1}{2}\text{ ft}$ unit cubes. The prism's dimensions are $2\text{ ft} \times 1\text{ ft} \times \tfrac{1}{2}\text{ ft}$ . How many of these $\tfrac{1}{2}$ -foot cubes fit exactly in the prism?
Answer: 8 This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh (multiply three edges) or V=bh (base area times height), understanding packing with fractional unit cubes gives same result. Volume V=lwh: multiply length, width, height (2 ft × 3 ft × (1/2) ft = 2×3×0.5=3 ft³, fractional edges multiply like any numbers). Or V=bh: base area l×w times height (base 5×4=20 m², height 2.5 m, volume 20×2.5=50 m³). Packing: fill prism with unit cubes (if edge 1/2 ft, unit cube is (1/2)³=1/8 ft³, box 2×1×(1/2) holds 2÷(1/2)×1÷(1/2)×(1/2)÷(1/2)=4×2×1=8 cubes of 1/8 ft³ each, total 8×(1/8)=1 ft³—same as V=lwh). Units: cubic (ft³, cm³, in³—length unit cubed). For this prism, number of cubes: (2/(1/2)) × (1/(1/2)) × ((1/2)/(1/2)) = 4×2×1=8. Common errors include multiplying dimensions instead of dividing or miscounting fits.
A cube-shaped block has edge length $\tfrac{1}{2}\text{ ft}$ . If you use cubes with edge length $\tfrac{1}{2}\text{ ft}$ as your unit cubes, how many unit cubes fit exactly inside the block?
Answer: 1 This question tests understanding packing rectangular prisms with fractional unit cubes, which relates to volume calculation V=lwh giving the same result. The block is a cube with edge 1/2 ft, and unit cubes are also 1/2 ft edge, so along each dimension: (1/2) ÷ (1/2) = 1, total 1×1×1=1 unit cube fits exactly. Volume-wise, V=(1/2)×(1/2)×(1/2)=1/8 ft³, and each unit cube is 1/8 ft³, so 1 fits. This validates that packing matches the formula. No units on choices, but implicitly number of cubes. Mistake like thinking volume 1/8 means 8 small cubes, but here unit is defined as 1/2 ft, not 1 ft. Steps: divide each edge by unit edge, 1×1×1=1.
A rectangular prism has a base area of $18\text{ cm}^2$ and a height of $\tfrac{2}{3}\text{ cm}$ . What is the volume? (Use $V=bh$ .)
Answer: $12\text{ cm}^3$ To calculate the volume of a rectangular prism with fractional edge lengths, use the formula $V = l \times w \times h$ , where you multiply the three dimensions, or $V = \text{base area} \times \text{height}$ , and understand that packing the prism with fractional unit cubes yields the same result. For example, with dimensions $2 \, \text{ft} \times 3 \, \text{ft} \times \frac{1}{2} \, \text{ft}$ , $V = 2 \times 3 \times 0.5 = 3 \, \text{ft}^3$ ; alternatively, using base area, if the base is $5 \, \text{m} \times 4 \, \text{m} = 20 \, \text{m}^2$ and height $2.5 \, \text{m}$ , then $V = 20 \times 2.5 = 50 \, \text{m}^3$ ; packing with $\frac{1}{2} \, \text{ft}$ cubes holds $24 \times \frac{1}{8} = 3 \, \text{ft}^3$ , units cubic like $\text{cm}^3$ . Another example: $2 \, \text{ft} \times 3 \, \text{ft} \times \frac{1}{2} \, \text{ft} = 3 \, \text{ft}^3$ ; $2.5 \, \text{cm} \times 4 \, \text{cm} \times 3 \, \text{cm} = 30 \, \text{cm}^3$ ; base $6 \times 5 = 30 \, \text{cm}^2$ $\times 2.5 \, \text{cm} = 75 \, \text{cm}^3$ . For this prism with base area $18 \, \text{cm}^2$ and height $\frac{2}{3} \, \text{cm}$ , $V = 18 \times \frac{2}{3} = \frac{36}{3} = 12 \, \text{cm}^3$ . Common errors include adding $18 + \frac{2}{3} \approx 18.67$ , using $\text{cm}^2$ , fraction wrong like $18 \div \frac{2}{3} = 27$ , or $18 \times \frac{3}{2} = 27$ inversely, or small like $\frac{2}{3}$ . Base-height method directly $V = bh = 18 \times \frac{2}{3} = 12$ ; fraction handling key. Packing verifies; real for small prisms; avoid adding, wrong units, fraction inversion, no multiplication.
A storage box is shaped like a rectangular prism with inside dimensions $2\text{ ft} \times 3\text{ ft} \times \tfrac{1}{2}\text{ ft}$ . What is the volume of the box in cubic feet? (Use $V=lwh$ .)
Answer: $3\text{ ft}^3$ This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh, where you multiply the three edges, and understanding that packing with fractional unit cubes yields the same result. For the storage box, the volume V=lwh means multiply length 2 ft, width 3 ft, and height 1/2 ft, so 2 × 3 × 0.5 = 6 × 0.5 = 3 ft³, and fractional edges multiply like any numbers. You could also think of it as base area times height, with base 2 ft × 3 ft = 6 ft² and height 0.5 ft, giving 6 × 0.5 = 3 ft³. Packing with unit cubes of edge 1/2 ft, each with volume (1/2)³ = 1/8 ft³, the box holds (2 ÷ 0.5) × (3 ÷ 0.5) × (0.5 ÷ 0.5) = 4 × 6 × 1 = 24 cubes, and 24 × (1/8) = 3 ft³, matching V=lwh. The units are cubic feet, ft³, since volume is length cubed. A common mistake is adding the dimensions instead of multiplying, like 2 + 3 + 0.5 = 5.5 ft³, or forgetting to cube the units, leading to 3 ft. To calculate correctly: identify l=2, w=3, h=0.5; multiply 2 × 3 × 0.5 = 3; add ft³.
A rectangular prism has base dimensions $3.2\text{ cm}$ by $1.5\text{ cm}$ and height $4\text{ cm}$ . What is the volume in cubic centimeters? (Use $V=bh$ .)
Answer: $19.2\text{ cm}^3$ This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh (multiply three edges) or V=bh (base area times height), understanding packing with fractional unit cubes gives same result. Volume V=lwh: multiply length, width, height (2 ft × 3 ft × (1/2) ft = 2×3×0.5=3 ft³, fractional edges multiply like any numbers). Or V=bh: base area l×w times height (base 3.2×1.5=4.8 cm², height 4 cm, volume 4.8×4=19.2 cm³). Packing: fill prism with unit cubes (if edge 1/2 ft, unit cube is (1/2)³=1/8 ft³, box 2×3×(1/2) holds 2÷(1/2)×3÷(1/2)×(1/2)÷(1/2)=4×6×1=24 cubes of 1/8 ft³ each, total 24×(1/8)=3 ft³—same as V=lwh). Units: cubic (ft³, cm³, in³—length unit cubed). For this prism, base=3.2×1.5=4.8 cm², V=4.8×4=19.2 cm³. Common errors include decimal multiplication mistakes or using square units.
A rectangular prism has a volume of $7\frac{1}{2}$ cubic inches. If the length is $2\frac{1}{2}$ inches and the width is $1\frac{1}{5}$ inches, what is the height of the prism?
Answer: $\frac{5}{2}$ inches Convert to improper fractions: Volume = $\frac{15}{2}$ , length = $\frac{5}{2}$ , width = $\frac{6}{5}$ . Using V = lwh: $\frac{15}{2} = \frac{5}{2} \times \frac{6}{5} \times h$ . First find $\frac{5}{2} \times \frac{6}{5} = \frac{30}{10} = 3$ . So $\frac{15}{2} = 3h$ , which gives $h = \frac{15}{2} \div 3 = \frac{15}{2} \times \frac{1}{3} = \frac{15}{6} = \frac{5}{2}$ inches. Choice B repeats the length value. Choice C uses incorrect division. Choice D results from calculation errors.
A rectangular prism has dimensions $\tfrac{3}{4}\text{ ft} \times 4\text{ ft} \times 2\text{ ft}$ . What is the volume of the prism in cubic feet? (Use $V=lwh$ .)
Answer: $6\text{ ft}^3$ This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh (multiply three edges) or V=bh (base area times height), understanding packing with fractional unit cubes gives same result. Volume V=lwh: multiply length, width, height (3/4 ft × 4 ft × 2 ft = (3/4)×4×2=6 ft³, fractional edges multiply like any numbers). Or V=bh: base area l×w times height (base 5×4=20 m², height 2.5 m, volume 20×2.5=50 m³). Packing: fill prism with unit cubes (if edge 1/2 ft, unit cube is (1/2)³=1/8 ft³, box 2×3×(1/2) holds 2÷(1/2)×3÷(1/2)×(1/2)÷(1/2)=4×6×1=24 cubes of 1/8 ft³ each, total 24×(1/8)=3 ft³—same as V=lwh). Units: cubic (ft³, cm³, in³—length unit cubed). For this prism, V=(3/4)×4×2=3×2=6 ft³. Common errors include improper fraction multiplication or adding dimensions.
A small gift box is a rectangular prism with dimensions $1\tfrac{1}{2}\text{ in} \times 2\text{ in} \times 3\text{ in}$ . What is the volume of the box in cubic inches?
Answer: $9\text{ in}^3$ This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh, where you multiply the three edges, and understanding that packing with fractional unit cubes yields the same result. Convert mixed number 1 1/2 in to 3/2 or 1.5 in, then V=1.5 × 2 × 3 = 3 × 3 = 9 in³. Or use V=bh with base 1.5 in × 2 in = 3 in², times height 3 in = 9 in³. Packing with 0.5 in cubes: along 1.5 in fits 3, along 2 in fits 4, along 3 in fits 6, total 3×4×6=72 cubes each (0.5)³=0.125 in³, 72×0.125=9 in³. Units are in³. Common mistakes include adding dimensions 1.5+2+3=6.5 (close to 6) or ignoring the fraction to get 1×2×3=6. Steps: convert 1 1/2 to 1.5; multiply 1.5×2×3=9; add in³.
A small science container is shaped like a rectangular prism measuring $2.5\text{ cm} \times 4\text{ cm} \times 3\text{ cm}$ . What is its volume?
Answer: $30\text{ cm}^3$ To calculate the volume of a rectangular prism with fractional edge lengths, use the formula V = l × w × h, where you multiply the three dimensions, or V = base area × height, and understand that packing the prism with fractional unit cubes yields the same result. For example, with dimensions 2 ft × 3 ft × (1/2) ft, V = 2 × 3 × 0.5 = 3 ft³; alternatively, using base area, if the base is 5 m × 4 m = 20 m² and height 2.5 m, then V = 20 × 2.5 = 50 m³; packing with 1/2 ft cubes in a 2 × 3 × (1/2) prism holds 4 × 6 × 1 = 24 cubes, each 1/8 ft³, totaling 3 ft³, with units always in cubic form like cm³. Another example: a prism 2 ft × 3 ft × (1/2) ft has V = 2 × 3 × (1/2) = 3 ft³; or 2.5 cm × 4 cm × 3 cm: V = 2.5 × 4 × 3 = 30 cm³; or base 6 × 5 = 30 cm², height 2.5 cm, V = 30 × 2.5 = 75 cm³. For this science container measuring 2.5 cm × 4 cm × 3 cm, the volume is 2.5 × 4 × 3 = 30 cm³. Common errors include adding dimensions like 2.5 + 4 + 3 = 9.5, forgetting cubic units to get 30 cm², mishandling decimals such as 2.5 × 4 = 100 incorrectly, using V = l + w + h, multiplying only two like 2.5 × 4 = 10 then forgetting 3, or errors like 2.5 × 4 = 1. For calculating, identify dimensions l=2.5, w=4, h=3, multiply as 2.5 × 4 = 10 then 10 × 3 = 30, and use cm³; mixed numbers convert to decimals like 1(1/2)=1.5 for multiplication. Base-height method: find base l × w, multiply by h; packing confirms formula; real uses include storage, aquariums, rooms; avoid adding, wrong units, fraction mishaps, missing dimensions, sum formulas.
A sandbox is shaped like a rectangular prism. Its base is $5\text{ m}$ by $4\text{ m}$ , and its height is $2.5\text{ m}$ . What is the volume of the sandbox in cubic meters? (Use $V=bh$ .)
Answer: $50\text{ m}^3$ This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh (multiply three edges) or V=bh (base area times height), understanding packing with fractional unit cubes gives same result. Volume V=lwh: multiply length, width, height (2 ft × 3 ft × (1/2) ft = 2×3×0.5=3 ft³, fractional edges multiply like any numbers). Or V=bh: base area l×w times height (base 5×4=20 m², height 2.5 m, volume 20×2.5=50 m³). Packing: fill prism with unit cubes (if edge 1/2 ft, unit cube is (1/2)³=1/8 ft³, box 2×3×(1/2) holds 2÷(1/2)×3÷(1/2)×(1/2)÷(1/2)=4×6×1=24 cubes of 1/8 ft³ each, total 24×(1/8)=3 ft³—same as V=lwh). Units: cubic (ft³, cm³, in³—length unit cubed). For this sandbox, base area=5×4=20 m², then V=20×2.5=50 m³. Common errors include using square units (50 m²) or miscalculating base area.
A rectangular prism has length $3\tfrac{3}{4}\text{ in}$ , width $2\text{ in}$ , and height $\tfrac{1}{2}\text{ in}$ . What is the volume in cubic inches?
Answer: $\tfrac{15}{4}\text{ in}^3$ This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh, where you multiply the three edges, and understanding that packing with fractional unit cubes yields the same result. Length 3 3/4 in=15/4 in, width 2 in, height 1/2 in, V=(15/4)×2×(1/2)=(15/4)×1=15/4 in³. Or base (15/4)×2=15/2 in², times 1/2=15/4 in³. Packing with 1/4 in cubes: along 15/4=3.75 fits 15, 2 fits 8, 0.5 fits 2, total 15×8×2=240 cubes each (1/4)³=1/64 in³, 240×1/64=240/64=15/4 in³. Units in³. Error like multiplying without simplifying (15/4)×2×(1/2)=15/4 but thinking it's 15/2. Steps: convert mixed to 15/4; multiply (15/4)×2×(1/2)=15/4 in³.
A rectangular prism is $2\tfrac{1}{2}\text{ cm}$ by $1\tfrac{1}{2}\text{ cm}$ by $2\text{ cm}$ . What is its volume in cubic centimeters?
Answer: $\tfrac{15}{2}\text{ cm}^3$ To calculate the volume of a rectangular prism with fractional edge lengths, use the formula V = l × w × h, where you multiply the three dimensions, or V = base area × height, and understand that packing the prism with fractional unit cubes yields the same result. For example, with dimensions 2 ft × 3 ft × (1/2) ft, V = 2 × 3 × 0.5 = 3 ft³; alternatively, using base area, if the base is 5 m × 4 m = 20 m² and height 2.5 m, then V = 20 × 2.5 = 50 m³; packing with 1/2 ft cubes holds 24 × 1/8 = 3 ft³, units cubic like cm³. Another example: 2 ft × 3 ft × (1/2) ft = 3 ft³; 2.5 cm × 4 cm × 3 cm = 30 cm³; base 6 × 5 = 30 cm² × 2.5 cm = 75 cm³. For this prism 2(1/2) cm=5/2 cm, 1(1/2) cm=3/2 cm, 2 cm, V=(5/2)×(3/2)×2=(15/4)×2=30/4=15/2 cm³. Common errors include adding 2.5+1.5+2=6, wrong multiplication like (5/2)×(3/2)=15/4 then ×2=15/2 but maybe to 9/2 or 15, or 2.5×1.5=3.75×2=7.5 but fraction 15/2 correct. Convert mixed to improper, multiply numerators 5×3×2=30, denominators 2×2×1=4, 30/4=15/2 cm³. Base-height: choose base ×h; packing verifies; real small items; avoid adding, fraction errors, no cubic, missing dimension.
A craft box is a rectangular prism that measures $0.6\text{ m} \times 0.5\text{ m} \times 0.4\text{ m}$ . What is its volume?
Answer: $0.12\text{ m}^3$ To calculate the volume of a rectangular prism with fractional edge lengths, use the formula V = l × w × h, where you multiply the three dimensions, or V = base area × height, and understand that packing the prism with fractional unit cubes yields the same result. For example, with dimensions 2 ft × 3 ft × (1/2) ft, V = 2 × 3 × 0.5 = 3 ft³; alternatively, using base area, if the base is 5 m × 4 m = 20 m² and height 2.5 m, then V = 20 × 2.5 = 50 m³; packing with 1/2 ft cubes holds 24 cubes of 1/8 ft³ for 3 ft³, units cubic like m³. Another example: 2 ft × 3 ft × (1/2) ft = 3 ft³; 2.5 cm × 4 cm × 3 cm = 30 cm³; base 6 × 5 = 30 cm² × 2.5 cm = 75 cm³. For this craft box 0.6 m × 0.5 m × 0.4 m, V = 0.6 × 0.5 × 0.4 = 0.3 × 0.4 = 0.12 m³. Common errors include adding 0.6+0.5+0.4=1.5, decimal mistakes like 0.6×0.5=0.3 then 0.3×0.4=1.2 or 0.15, using m², sum formula, two dimensions only like 0.6×0.5=0.3 forgetting 0.4. Calculate by multiplying step-by-step 0.6×0.5=0.3, 0.3×0.4=0.12 m³; decimals like fractions. Base-height: base ×h; packing verifies; real craft storage; avoid adding, decimal errors, no cubic, missing dimension.
A science lab container is a rectangular prism that measures $2.5\text{ cm} \times 4\text{ cm} \times 3\text{ cm}$ . What is its volume in cubic centimeters? (Use $V=lwh$ .)
Answer: $30\text{ cm}^3$ This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh (multiply three edges) or V=bh (base area times height), understanding packing with fractional unit cubes gives same result. Volume V=lwh: multiply length, width, height (2.5 cm × 4 cm × 3 cm = 2.5×4×3=30 cm³, fractional edges multiply like any numbers). Or V=bh: base area l×w times height (base 5×4=20 m², height 2.5 m, volume 20×2.5=50 m³). Packing: fill prism with unit cubes (if edge 1/2 ft, unit cube is (1/2)³=1/8 ft³, box 2×3×(1/2) holds 2÷(1/2)×3÷(1/2)×(1/2)÷(1/2)=4×6×1=24 cubes of 1/8 ft³ each, total 24×(1/8)=3 ft³—same as V=lwh). Units: cubic (ft³, cm³, in³—length unit cubed). For this container, V=2.5×4×3=10×3=30 cm³. Common errors include multiplying only two dimensions (2.5×4=10) or using square units (30 cm²).
A rectangular prism has a base that is $5\text{ m}$ by $4\text{ m}$ and a height of $2.5\text{ m}$ . What is the volume of the prism in cubic meters? (Use $V=bh$ .)
Answer: $50\text{ m}^3$ This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=bh, base area times height, and understanding that packing with fractional unit cubes gives the same result. Base is 5 m × 4 m = 20 m², height 2.5 m, so V=20 × 2.5 = 50 m³. Alternatively, as V=lwh: 5 × 4 × 2.5 = 20 × 2.5 = 50 m³. Packing with 0.5 m cubes: along 5 m fits 10, 4 m fits 8, 2.5 m fits 5, total 10×8×5=400 cubes each (0.5)³=0.125 m³, 400×0.125=50 m³. Units m³. Error like multiplying only base 5×4=20, forgetting height, or adding 5+4+2.5=11.5 (not matching choices). Calculate: base 20 m² × 2.5 m = 50 m³.
A rectangular prism is $1\text{ ft}$ long, $\tfrac{1}{2}\text{ ft}$ wide, and $\tfrac{1}{2}\text{ ft}$ tall. If you pack it completely with cubes that each have edge length $\tfrac{1}{2}\text{ ft}$ , how many such cubes fit inside?
Answer: 2 To calculate the volume of a rectangular prism with fractional edge lengths, use the formula V = l × w × h, where you multiply the three dimensions, or V = base area × height, and understand that packing the prism with fractional unit cubes yields the same result. For example, with dimensions 2 ft × 3 ft × (1/2) ft, V = 2 × 3 × 0.5 = 3 ft³; alternatively, using base area, if the base is 5 m × 4 m = 20 m² and height 2.5 m, then V = 20 × 2.5 = 50 m³; packing with 1/2 ft cubes in a 2 × 3 × (1/2) prism holds 4 × 6 × 1 = 24 cubes, each 1/8 ft³, totaling 3 ft³, with units always in cubic form like ft³ though here it's count. Another example: a prism 2 ft × 3 ft × (1/2) ft has V = 2 × 3 × (1/2) = 3 ft³; or 2.5 cm × 4 cm × 3 cm: V = 30 cm³; or base 6 × 5 = 30 cm², height 2.5 cm, V = 75 cm³. For this prism 1 ft × (1/2) ft × (1/2) ft packed with (1/2) ft cubes, along length 1/(1/2)=2, width (1/2)/(1/2)=1, height (1/2)/(1/2)=1, so 2 × 1 × 1 = 2 cubes. Common errors include thinking volume is 1 × 0.5 × 0.5 = 0.25 then dividing wrong to 1 or 8, confusing with cube volume $(1/2)^3$ =1/8 then miscounting to 4, adding, or ignoring packing. To calculate packing, divide each dimension by cube edge: 1/(0.5)=2, etc., multiply counts 2×1×1=2; relates to V / cube volume = (0.25) / (0.125) = 2. Packing verifies formula; real for storage; avoid misdividing, confusing volume with count, adding, wrong units.
Refer to the diagram. A company manufactures wooden blocks in two different sizes. Block A has dimensions shown, and Block B has each dimension exactly $\frac{1}{2}$ the size of Block A's corresponding dimension. How many Block B pieces have the same total volume as 4 Block A pieces?
Answer: 32 Block B pieces When each dimension is scaled by $\frac{1}{2}$ , the volume is scaled by $\left(\frac{1}{2}\right)^3 = \frac{1}{8}$ . So Block B has $\frac{1}{8}$ the volume of Block A. To equal the volume of 4 Block A pieces, we need $4 ÷ \frac{1}{8} = 4 \times 8 = 32$ Block B pieces. Choice A uses linear scaling. Choice B uses area scaling. Choice D incorrectly multiplies by 12.
A rectangular prism can be packed exactly with cubes that each have edge length $0.5\text{ cm}$ . The prism's dimensions are $2\text{ cm} \times 1.5\text{ cm} \times 1\text{ cm}$ . How many of the $0.5\text{ cm}$ cubes fit inside the prism?
Answer: 24 This question tests understanding packing rectangular prisms with fractional unit cubes, which validates volume V=lwh by giving the same result. Prism 2 cm × 1.5 cm × 1 cm, unit cubes 0.5 cm edge: along 2 cm fits 4, 1.5 cm fits 3, 1 cm fits 2, total 4×3×2=24 cubes. Volume-wise, V=2×1.5×1=3 cm³, each cube (0.5)³=0.125 cm³, 3÷0.125=24 cubes. This shows packing matches formula. No units on choices, but number of cubes. Mistake like multiplying dimensions without dividing, 2×1.5×1=3, or adding to 4.5÷0.5=9 (close to choices). Steps: divide each dimension by 0.5, get 4,3,2; multiply 4×3×2=24.
A rectangular prism has a base area of $12\tfrac{1}{2}\text{ cm}^2$ and a height of $\tfrac{4}{5}\text{ cm}$ . What is the volume of the prism in cubic centimeters? (Use $V=bh$ .)
Answer: $10\text{ cm}^3$ Finding the volume of a prism is like stacking layers! The formula $V = b h$ tells us to multiply the base area by the height. Let's use our numbers. First, turn the mixed number into a fraction: $12\tfrac{1}{2} = \frac{25}{2}$ The height is already a fraction: $\frac{4}{5}$ . Now multiply across the tops and across the bottoms: $V = \frac{25}{2} \times \frac{4}{5} = \frac{25 \times 4}{2 \times 5} = \frac{100}{10} = 10$ Since we are measuring space inside a 3-D shape, the units are cubic centimeters: $10\text{ cm}^3$ . Think of the base as the floor of a box, and the height as how tall you stack that floor. Multiply them, and you fill the whole box! Try this at home: Pick a base area and a fraction height, then multiply them like fractions to find your own volume. 📦
Maria is building a concrete foundation that measures $3\frac{1}{2}$ yards long, $2\frac{1}{4}$ yards wide, and $\frac{2}{3}$ yards thick. Concrete costs $45 per cubic yard. What is the total cost of the concrete needed for this foundation?
Answer: $236.25 First convert mixed numbers: $3\frac{1}{2} = \frac{7}{2}$ and $2\frac{1}{4} = \frac{9}{4}$ . Volume = $\frac{7}{2} \times \frac{9}{4} \times \frac{2}{3} = \frac{7 \times 9 \times 2}{2 \times 4 \times 3} = \frac{126}{24} = \frac{21}{4} = 5.25$ cubic yards. Cost = $5.25 \times 45 = 236.25$ . Choice B uses incorrect conversion of mixed numbers. Choice C doubles the correct volume. Choice D uses wrong dimension calculations.

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