Find Prism Volume by Packing - 5th Grade Math
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Find the missing base area $B$ if $V=56$ cubic units and height $h=7$ units.
Find the missing base area $B$ if $V=56$ cubic units and height $h=7$ units.
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$B = 8$ square units. Divide volume by height: $56 \div 7$.
$B = 8$ square units. Divide volume by height: $56 \div 7$.
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Find the missing edge length $w$ if $V=48$, $l=6$, and $h=4$ for a right rectangular prism.
Find the missing edge length $w$ if $V=48$, $l=6$, and $h=4$ for a right rectangular prism.
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$w = 2$ units. Solve $48 = 6 \times w \times 4$ for $w$.
$w = 2$ units. Solve $48 = 6 \times w \times 4$ for $w$.
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State the formula for volume using base area $B$ and height $h$ for a right rectangular prism.
State the formula for volume using base area $B$ and height $h$ for a right rectangular prism.
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$V = B \times h$. Base area times height gives volume.
$V = B \times h$. Base area times height gives volume.
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What unit is used for the volume of a prism when edge lengths are measured in units?
What unit is used for the volume of a prism when edge lengths are measured in units?
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Cubic units, $\text{units}^3$. Volume is 3-dimensional, so units are cubed.
Cubic units, $\text{units}^3$. Volume is 3-dimensional, so units are cubed.
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What is the formula for the area of the rectangular base if the base edges are $l$ and $w$?
What is the formula for the area of the rectangular base if the base edges are $l$ and $w$?
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$B = l \times w$. Rectangle area is length times width.
$B = l \times w$. Rectangle area is length times width.
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A prism has volume $V=72$ and base area $B=9$. What is the height $h$?
A prism has volume $V=72$ and base area $B=9$. What is the height $h$?
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$h = 8$. Solve $72 = 9 \times h$ by dividing.
$h = 8$. Solve $72 = 9 \times h$ by dividing.
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How many unit cubes fill one layer of a prism with base edges $l=5$ and $w=4$?
How many unit cubes fill one layer of a prism with base edges $l=5$ and $w=4$?
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$20$ unit cubes per layer. One layer has $l \times w = 5 \times 4$ cubes.
$20$ unit cubes per layer. One layer has $l \times w = 5 \times 4$ cubes.
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A prism has $l=5$, $w=4$, and $h=3$. How many unit cubes fill the prism?
A prism has $l=5$, $w=4$, and $h=3$. How many unit cubes fill the prism?
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$60$ unit cubes. Total cubes equals $l \times w \times h = 5 \times 4 \times 3$.
$60$ unit cubes. Total cubes equals $l \times w \times h = 5 \times 4 \times 3$.
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Which expression matches the associative property for prism volume: $(l \times w) \times h$ or $l \times (w \times h)$?
Which expression matches the associative property for prism volume: $(l \times w) \times h$ or $l \times (w \times h)$?
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Both; $(l \times w) \times h = l \times (w \times h)$. Associative property: grouping doesn't change product.
Both; $(l \times w) \times h = l \times (w \times h)$. Associative property: grouping doesn't change product.
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Compute the volume using associativity: $(2 \times 6) \times 5$ cubic units.
Compute the volume using associativity: $(2 \times 6) \times 5$ cubic units.
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$60$ cubic units. Calculate: $12 \times 5 = 60$.
$60$ cubic units. Calculate: $12 \times 5 = 60$.
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Compute the volume using base area first: $(8 \times 3) \times 2$ cubic units.
Compute the volume using base area first: $(8 \times 3) \times 2$ cubic units.
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$48$ cubic units. Calculate: $24 \times 2 = 48$.
$48$ cubic units. Calculate: $24 \times 2 = 48$.
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Identify the error: A student says $V = l + w + h$ for a prism. What is the correct formula?
Identify the error: A student says $V = l + w + h$ for a prism. What is the correct formula?
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Correct: $V = l \times w \times h$. Addition gives perimeter, not volume.
Correct: $V = l \times w \times h$. Addition gives perimeter, not volume.
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A prism has $l=9$, $w=1$, and $h=8$. What threefold product represents its volume?
A prism has $l=9$, $w=1$, and $h=8$. What threefold product represents its volume?
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$9 \times 1 \times 8 = 72$. Shows volume as a threefold product.
$9 \times 1 \times 8 = 72$. Shows volume as a threefold product.
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What does packing a prism with $1 \times 1 \times 1$ cubes measure?
What does packing a prism with $1 \times 1 \times 1$ cubes measure?
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The volume in unit cubes. Unit cubes directly show how many fit inside.
The volume in unit cubes. Unit cubes directly show how many fit inside.
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Identify the three dimensions multiplied to find a right rectangular prism’s volume.
Identify the three dimensions multiplied to find a right rectangular prism’s volume.
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Length, width, and height. Three perpendicular edges define the prism.
Length, width, and height. Three perpendicular edges define the prism.
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Find the volume of a prism with $l=4$, $w=3$, and $h=2$.
Find the volume of a prism with $l=4$, $w=3$, and $h=2$.
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$24$ cubic units. Apply $V = l \times w \times h = 4 \times 3 \times 2$.
$24$ cubic units. Apply $V = l \times w \times h = 4 \times 3 \times 2$.
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Find the volume of a prism with base area $B=15$ and height $h=4$.
Find the volume of a prism with base area $B=15$ and height $h=4$.
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$60$ cubic units. Apply $V = B \times h = 15 \times 4$.
$60$ cubic units. Apply $V = B \times h = 15 \times 4$.
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A prism has $l=7$, $w=2$, and $h=3$. What is its volume?
A prism has $l=7$, $w=2$, and $h=3$. What is its volume?
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$42$ cubic units. Apply $V = 7 \times 2 \times 3$.
$42$ cubic units. Apply $V = 7 \times 2 \times 3$.
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A prism has $B=24$ and $h=2$. What is its volume?
A prism has $B=24$ and $h=2$. What is its volume?
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$48$ cubic units. Apply $V = B \times h = 24 \times 2$.
$48$ cubic units. Apply $V = B \times h = 24 \times 2$.
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A prism has volume $V=56$, width $w=2$, and height $h=7$. What is the length $l$?
A prism has volume $V=56$, width $w=2$, and height $h=7$. What is the length $l$?
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$l = 4$. Solve $56 = l \times 2 \times 7$ for $l$.
$l = 4$. Solve $56 = l \times 2 \times 7$ for $l$.
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