Rectangular Prism Volume - SSAT Middle Level: Quantitative
Card 1 of 23
If $l$, $w$, and $h$ each double, what happens to the volume $V$?
If $l$, $w$, and $h$ each double, what happens to the volume $V$?
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The volume becomes $8V$. Doubling all dimensions scales volume by $2^3 = 8$, as volume is cubic.
The volume becomes $8V$. Doubling all dimensions scales volume by $2^3 = 8$, as volume is cubic.
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Identify the error: A student wrote $V = 2l + 2w + 2h$ for a rectangular prism’s volume. What is correct?
Identify the error: A student wrote $V = 2l + 2w + 2h$ for a rectangular prism’s volume. What is correct?
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Correct formula: $V = lwh$. The student's formula is for perimeter of the faces, not volume, which requires multiplication of dimensions.
Correct formula: $V = lwh$. The student's formula is for perimeter of the faces, not volume, which requires multiplication of dimensions.
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A box measures $30\text{ cm}$ by $20\text{ cm}$ by $10\text{ cm}$. What is its volume in $\text{cm}^3$?
A box measures $30\text{ cm}$ by $20\text{ cm}$ by $10\text{ cm}$. What is its volume in $\text{cm}^3$?
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$6000\text{ cm}^3$. Volume is the product of dimensions: $30 \times 20 \times 10 = 6000$ cubic centimeters.
$6000\text{ cm}^3$. Volume is the product of dimensions: $30 \times 20 \times 10 = 6000$ cubic centimeters.
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A prism has dimensions $4\text{ ft}$ by $3\text{ ft}$ by $2\text{ ft}$. What is its volume in $\text{ft}^3$?
A prism has dimensions $4\text{ ft}$ by $3\text{ ft}$ by $2\text{ ft}$. What is its volume in $\text{ft}^3$?
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$24\text{ ft}^3$. Multiply dimensions for volume: $4 \times 3 \times 2 = 24$ cubic feet.
$24\text{ ft}^3$. Multiply dimensions for volume: $4 \times 3 \times 2 = 24$ cubic feet.
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What is the formula for volume written as base area $B$ times height $h$ for a rectangular prism?
What is the formula for volume written as base area $B$ times height $h$ for a rectangular prism?
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$V = Bh$. For prisms, volume is the product of the base area and the height perpendicular to that base.
$V = Bh$. For prisms, volume is the product of the base area and the height perpendicular to that base.
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What is the base area $B$ of a rectangular prism with base length $l$ and base width $w$?
What is the base area $B$ of a rectangular prism with base length $l$ and base width $w$?
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$B = lw$. The base area of a rectangular prism is the area of its rectangular base, found by multiplying length and width.
$B = lw$. The base area of a rectangular prism is the area of its rectangular base, found by multiplying length and width.
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What are the correct cubic units for the volume of a rectangular prism measured in centimeters?
What are the correct cubic units for the volume of a rectangular prism measured in centimeters?
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cubic centimeters, $\text{cm}^3$. Volume measures three-dimensional space, so units are the linear unit raised to the third power.
cubic centimeters, $\text{cm}^3$. Volume measures three-dimensional space, so units are the linear unit raised to the third power.
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What is the volume of a rectangular prism with $l = 5$, $w = 3$, and $h = 4$?
What is the volume of a rectangular prism with $l = 5$, $w = 3$, and $h = 4$?
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$60$. Volume is the product of length, width, and height: $5 \times 3 \times 4 = 60$.
$60$. Volume is the product of length, width, and height: $5 \times 3 \times 4 = 60$.
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What is the volume of a rectangular prism with dimensions $8\text{ m}$ by $2\text{ m}$ by $3\text{ m}$?
What is the volume of a rectangular prism with dimensions $8\text{ m}$ by $2\text{ m}$ by $3\text{ m}$?
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$48\text{ m}^3$. Multiply the three dimensions: $8 \times 2 \times 3 = 48$, with cubic meter units.
$48\text{ m}^3$. Multiply the three dimensions: $8 \times 2 \times 3 = 48$, with cubic meter units.
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What is the volume of a rectangular prism with $l = 10$, $w = 2$, and $h = 1$?
What is the volume of a rectangular prism with $l = 10$, $w = 2$, and $h = 1$?
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$20$. Volume equals length times width times height: $10 \times 2 \times 1 = 20$.
$20$. Volume equals length times width times height: $10 \times 2 \times 1 = 20$.
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What is the volume of a rectangular prism with $l = 6$, $w = 6$, and $h = 2$?
What is the volume of a rectangular prism with $l = 6$, $w = 6$, and $h = 2$?
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$72$. Calculate by multiplying dimensions: $6 \times 6 \times 2 = 72$.
$72$. Calculate by multiplying dimensions: $6 \times 6 \times 2 = 72$.
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What is the volume of a rectangular prism with $l = 9$, $w = 4$, and $h = 5$?
What is the volume of a rectangular prism with $l = 9$, $w = 4$, and $h = 5$?
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$180$. The product of the dimensions gives volume: $9 \times 4 \times 5 = 180$.
$180$. The product of the dimensions gives volume: $9 \times 4 \times 5 = 180$.
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A prism has base area $B = 12$ and height $h = 7$. What is its volume?
A prism has base area $B = 12$ and height $h = 7$. What is its volume?
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$84$. Volume is base area times height: $12 \times 7 = 84$.
$84$. Volume is base area times height: $12 \times 7 = 84$.
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A rectangular prism has volume $V = 96$, length $l = 8$, and width $w = 4$. What is height $h$?
A rectangular prism has volume $V = 96$, length $l = 8$, and width $w = 4$. What is height $h$?
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$3$. Solve for height by dividing volume by the product of length and width: $h = \frac{96}{8 \times 4}$.
$3$. Solve for height by dividing volume by the product of length and width: $h = \frac{96}{8 \times 4}$.
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A rectangular prism has volume $V = 72$, width $w = 3$, and height $h = 4$. What is length $l$?
A rectangular prism has volume $V = 72$, width $w = 3$, and height $h = 4$. What is length $l$?
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$6$. Find length by dividing volume by width times height: $l = \frac{72}{3 \times 4}$.
$6$. Find length by dividing volume by width times height: $l = \frac{72}{3 \times 4}$.
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A rectangular prism has volume $V = 150$, length $l = 10$, and height $h = 5$. What is width $w$?
A rectangular prism has volume $V = 150$, length $l = 10$, and height $h = 5$. What is width $w$?
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$3$. Determine width by dividing volume by length times height: $w = \frac{150}{10 \times 5}$.
$3$. Determine width by dividing volume by length times height: $w = \frac{150}{10 \times 5}$.
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A rectangular prism has $V = 24\text{ in}^3$, $l = 4\text{ in}$, $w = 2\text{ in}$. What is $h$?
A rectangular prism has $V = 24\text{ in}^3$, $l = 4\text{ in}$, $w = 2\text{ in}$. What is $h$?
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$3\text{ in}$. Height is volume divided by length times width: $h = \frac{24}{4 \times 2}$, in inches.
$3\text{ in}$. Height is volume divided by length times width: $h = \frac{24}{4 \times 2}$, in inches.
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What is the volume of a rectangular prism with $l = \frac{1}{2}$, $w = 6$, and $h = 4$?
What is the volume of a rectangular prism with $l = \frac{1}{2}$, $w = 6$, and $h = 4$?
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$12$. Multiply fractional and whole number dimensions: $\frac{1}{2} \times 6 \times 4 = 12$.
$12$. Multiply fractional and whole number dimensions: $\frac{1}{2} \times 6 \times 4 = 12$.
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What is the volume of a rectangular prism with $l = 3$, $w = \frac{2}{3}$, and $h = 9$?
What is the volume of a rectangular prism with $l = 3$, $w = \frac{2}{3}$, and $h = 9$?
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$18$. Volume computation includes fractions: $3 \times \frac{2}{3} \times 9 = 18$.
$18$. Volume computation includes fractions: $3 \times \frac{2}{3} \times 9 = 18$.
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What is the volume of a rectangular prism with $l = 2.5$, $w = 4$, and $h = 3$?
What is the volume of a rectangular prism with $l = 2.5$, $w = 4$, and $h = 3$?
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$30$. Handle decimal dimensions by multiplication: $2.5 \times 4 \times 3 = 30$.
$30$. Handle decimal dimensions by multiplication: $2.5 \times 4 \times 3 = 30$.
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What is the volume of a rectangular prism with $l = 1.2$, $w = 5$, and $h = 2$?
What is the volume of a rectangular prism with $l = 1.2$, $w = 5$, and $h = 2$?
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$12$. Decimal multiplication yields volume: $1.2 \times 5 \times 2 = 12$.
$12$. Decimal multiplication yields volume: $1.2 \times 5 \times 2 = 12$.
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If $l$ doubles while $w$ and $h$ stay the same, how does the volume $V$ change?
If $l$ doubles while $w$ and $h$ stay the same, how does the volume $V$ change?
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The volume doubles, $V \to 2V$. Since volume is proportional to length, doubling length multiplies volume by 2.
The volume doubles, $V \to 2V$. Since volume is proportional to length, doubling length multiplies volume by 2.
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If $h$ is cut in half while $l$ and $w$ stay the same, how does the volume $V$ change?
If $h$ is cut in half while $l$ and $w$ stay the same, how does the volume $V$ change?
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The volume becomes $\frac{1}{2}V$. Halving height multiplies volume by $\frac{1}{2}$, due to direct proportionality.
The volume becomes $\frac{1}{2}V$. Halving height multiplies volume by $\frac{1}{2}$, due to direct proportionality.
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