Find Volume With Fractional Edge Lengths - 6th Grade Math
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How many cubes of edge $\frac{1}{4}$ fit along an edge of length $\frac{3}{4}$?
How many cubes of edge $\frac{1}{4}$ fit along an edge of length $\frac{3}{4}$?
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$3$ cubes. Divide edge length by cube size: $\frac{3/4}{1/4} = \frac{3}{4} \cdot 4 = 3$.
$3$ cubes. Divide edge length by cube size: $\frac{3/4}{1/4} = \frac{3}{4} \cdot 4 = 3$.
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A box is $\frac{2}{3}$ ft by $\frac{3}{4}$ ft by $\frac{1}{2}$ ft. Find its volume.
A box is $\frac{2}{3}$ ft by $\frac{3}{4}$ ft by $\frac{1}{2}$ ft. Find its volume.
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$\frac{1}{4},\text{ft}^3$. Apply $V=lwh$: $\frac{2}{3} \cdot \frac{3}{4} \cdot \frac{1}{2} = \frac{6}{24} = \frac{1}{4}$.
$\frac{1}{4},\text{ft}^3$. Apply $V=lwh$: $\frac{2}{3} \cdot \frac{3}{4} \cdot \frac{1}{2} = \frac{6}{24} = \frac{1}{4}$.
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What is the volume of one unit cube with edge length $\frac{1}{5}$?
What is the volume of one unit cube with edge length $\frac{1}{5}$?
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$\frac{1}{125}$ cubic unit. Volume of a cube = edge³ = $(\frac{1}{5})^3 = \frac{1}{125}$.
$\frac{1}{125}$ cubic unit. Volume of a cube = edge³ = $(\frac{1}{5})^3 = \frac{1}{125}$.
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Identify the unit cube edge length: a cube has volume $\frac{1}{27}$ cubic unit.
Identify the unit cube edge length: a cube has volume $\frac{1}{27}$ cubic unit.
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edge length $=\frac{1}{3}$. Since $V = s^3$, if $s^3 = \frac{1}{27}$, then $s = \frac{1}{3}$.
edge length $=\frac{1}{3}$. Since $V = s^3$, if $s^3 = \frac{1}{27}$, then $s = \frac{1}{3}$.
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How many $\left(\frac{1}{4}\right)^3$ cubes fill a prism $\frac{1}{2}\times\frac{3}{4}\times 1$?
How many $\left(\frac{1}{4}\right)^3$ cubes fill a prism $\frac{1}{2}\times\frac{3}{4}\times 1$?
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$24$ cubes. $(\frac{1/2}{1/4}) \cdot (\frac{3/4}{1/4}) \cdot (\frac{1}{1/4}) = 2 \cdot 3 \cdot 4 = 24$.
$24$ cubes. $(\frac{1/2}{1/4}) \cdot (\frac{3/4}{1/4}) \cdot (\frac{1}{1/4}) = 2 \cdot 3 \cdot 4 = 24$.
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Choose the correct expression for volume: $l=\frac{2}{5}$, $w=\frac{3}{4}$, $h=\frac{1}{2}$.
Choose the correct expression for volume: $l=\frac{2}{5}$, $w=\frac{3}{4}$, $h=\frac{1}{2}$.
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$V=\frac{2}{5}\cdot\frac{3}{4}\cdot\frac{1}{2}$. The volume formula requires multiplying all three dimensions together.
$V=\frac{2}{5}\cdot\frac{3}{4}\cdot\frac{1}{2}$. The volume formula requires multiplying all three dimensions together.
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Find and correct the error: A student wrote $V=lw+h$ for a right rectangular prism.
Find and correct the error: A student wrote $V=lw+h$ for a right rectangular prism.
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Correct: $V=lwh$. Volume requires multiplication, not addition, of the three dimensions.
Correct: $V=lwh$. Volume requires multiplication, not addition, of the three dimensions.
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Find the missing height: $V=\frac{3}{10}$, $l=\frac{3}{5}$, $w=\frac{1}{2}$.
Find the missing height: $V=\frac{3}{10}$, $l=\frac{3}{5}$, $w=\frac{1}{2}$.
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$h=1$. Solve: $\frac{3}{10} = \frac{3}{5} \cdot \frac{1}{2} \cdot h$; $h = \frac{3/10}{3/10} = 1$.
$h=1$. Solve: $\frac{3}{10} = \frac{3}{5} \cdot \frac{1}{2} \cdot h$; $h = \frac{3/10}{3/10} = 1$.
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Find the missing width: $V=\frac{1}{6}$, $l=\frac{1}{2}$, $h=\frac{2}{3}$.
Find the missing width: $V=\frac{1}{6}$, $l=\frac{1}{2}$, $h=\frac{2}{3}$.
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$w=\frac{1}{2}$. Solve: $\frac{1}{6} = \frac{1}{2} \cdot w \cdot \frac{2}{3}$; $w = \frac{ \frac{1}{6} }{ \frac{1}{3} } = \frac{1}{2}$
$w=\frac{1}{2}$. Solve: $\frac{1}{6} = \frac{1}{2} \cdot w \cdot \frac{2}{3}$; $w = \frac{ \frac{1}{6} }{ \frac{1}{3} } = \frac{1}{2}$
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Find the base area: $l=\frac{5}{6}$ and $w=\frac{3}{10}$.
Find the base area: $l=\frac{5}{6}$ and $w=\frac{3}{10}$.
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$\frac{1}{4}$ square units. Base area = length × width = $\frac{5}{6} \cdot \frac{3}{10} = \frac{15}{60} = \frac{1}{4}$.
$\frac{1}{4}$ square units. Base area = length × width = $\frac{5}{6} \cdot \frac{3}{10} = \frac{15}{60} = \frac{1}{4}$.
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What unit should be used for volume if edge lengths are measured in inches?
What unit should be used for volume if edge lengths are measured in inches?
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cubic inches, $\text{in}^3$. Volume units are always the cube of the linear measurement unit.
cubic inches, $\text{in}^3$. Volume units are always the cube of the linear measurement unit.
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Find the volume using $V=Bh$: $B=\frac{7}{12}$ and $h=\frac{2}{7}$.
Find the volume using $V=Bh$: $B=\frac{7}{12}$ and $h=\frac{2}{7}$.
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$\frac{1}{6}$ cubic units. Apply $V=Bh$: $\frac{7}{12} \cdot \frac{2}{7} = \frac{14}{84} = \frac{1}{6}$.
$\frac{1}{6}$ cubic units. Apply $V=Bh$: $\frac{7}{12} \cdot \frac{2}{7} = \frac{14}{84} = \frac{1}{6}$.
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How many $\left(\frac{1}{2}\right)^3$ unit cubes fill a $1\times 1\times 1$ cube?
How many $\left(\frac{1}{2}\right)^3$ unit cubes fill a $1\times 1\times 1$ cube?
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$8$ cubes. Each dimension fits $\frac{1}{\frac{1}{2}} = 2$ cubes, so $2^3 = 8$ total.
$8$ cubes. Each dimension fits $\frac{1}{\frac{1}{2}} = 2$ cubes, so $2^3 = 8$ total.
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How many $\left(\frac{1}{3}\right)^3$ unit cubes fill a $1\times 1\times 1$ cube?
How many $\left(\frac{1}{3}\right)^3$ unit cubes fill a $1\times 1\times 1$ cube?
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$27$ cubes. Each dimension fits $\frac{1}{\frac{1}{3}} = 3$ cubes, so $3^3 = 27$ total.
$27$ cubes. Each dimension fits $\frac{1}{\frac{1}{3}} = 3$ cubes, so $3^3 = 27$ total.
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What does $B$ represent in the formula $V=Bh$ for a right rectangular prism?
What does $B$ represent in the formula $V=Bh$ for a right rectangular prism?
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$B$ is the area of the base. In $V=Bh$, $B$ represents the two-dimensional area of the prism's base.
$B$ is the area of the base. In $V=Bh$, $B$ represents the two-dimensional area of the prism's base.
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State the volume formula for a right rectangular prism using base area and height.
State the volume formula for a right rectangular prism using base area and height.
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$V=Bh$. Volume equals base area times height for any prism.
$V=Bh$. Volume equals base area times height for any prism.
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Find the volume: $l=\frac{3}{4}$, $w=\frac{2}{3}$, $h=\frac{1}{2}$.
Find the volume: $l=\frac{3}{4}$, $w=\frac{2}{3}$, $h=\frac{1}{2}$.
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$\frac{1}{4}$ cubic units. Multiply: $\frac{3}{4} \cdot \frac{2}{3} \cdot \frac{1}{2} = \frac{6}{24} = \frac{1}{4}$.
$\frac{1}{4}$ cubic units. Multiply: $\frac{3}{4} \cdot \frac{2}{3} \cdot \frac{1}{2} = \frac{6}{24} = \frac{1}{4}$.
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Find the volume: $l=\frac{1}{2}$, $w=\frac{1}{3}$, $h=\frac{1}{4}$.
Find the volume: $l=\frac{1}{2}$, $w=\frac{1}{3}$, $h=\frac{1}{4}$.
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$\frac{1}{24}$ cubic units. Multiply: $\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{4} = \frac{1}{24}$.
$\frac{1}{24}$ cubic units. Multiply: $\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{4} = \frac{1}{24}$.
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State the volume formula for a right rectangular prism using length, width, and height.
State the volume formula for a right rectangular prism using length, width, and height.
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$V=lwh$. Volume equals length times width times height for rectangular prisms.
$V=lwh$. Volume equals length times width times height for rectangular prisms.
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Find the volume: $l=1\frac{1}{2}$, $w=\frac{2}{3}$, $h=\frac{3}{4}$.
Find the volume: $l=1\frac{1}{2}$, $w=\frac{2}{3}$, $h=\frac{3}{4}$.
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$\frac{3}{4}$ cubic units. Convert: $1\frac{1}{2} = \frac{3}{2}$, then $\frac{3}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} = \frac{18}{24} = \frac{3}{4}$.
$\frac{3}{4}$ cubic units. Convert: $1\frac{1}{2} = \frac{3}{2}$, then $\frac{3}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} = \frac{18}{24} = \frac{3}{4}$.
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Identify the volume of a prism $1 imes rac{1}{2} imes rac{3}{2}$ in cubic units.
Identify the volume of a prism $1 imes rac{1}{2} imes rac{3}{2}$ in cubic units.
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$ rac{3}{4}$ cubic unit. Apply $V = lwh = 1 imes rac{1}{2} imes rac{3}{2} = rac{3}{4}$.
$ rac{3}{4}$ cubic unit. Apply $V = lwh = 1 imes rac{1}{2} imes rac{3}{2} = rac{3}{4}$.
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Identify the missing height $h$ if $V= rac{3}{4}$ and $b= rac{1}{2}$ for a right rectangular prism.
Identify the missing height $h$ if $V= rac{3}{4}$ and $b= rac{1}{2}$ for a right rectangular prism.
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$h= rac{3}{2}$. Solve $V = bh$: $ rac{3}{4} = rac{1}{2} imes h$, so $h = rac{3}{2}$.
$h= rac{3}{2}$. Solve $V = bh$: $ rac{3}{4} = rac{1}{2} imes h$, so $h = rac{3}{2}$.
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Identify the missing width $w$ if $V=3$, $l=2$, and $h= rac{3}{4}$ for a right rectangular prism.
Identify the missing width $w$ if $V=3$, $l=2$, and $h= rac{3}{4}$ for a right rectangular prism.
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$w=2$. Solve $V = lwh$: $3 = 2 imes w imes rac{3}{4}$, so $w = 2$.
$w=2$. Solve $V = lwh$: $3 = 2 imes w imes rac{3}{4}$, so $w = 2$.
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Which expression correctly represents the volume of a prism with edges $ rac{2}{3}$, $ rac{3}{5}$, and $ rac{5}{2}$?
Which expression correctly represents the volume of a prism with edges $ rac{2}{3}$, $ rac{3}{5}$, and $ rac{5}{2}$?
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$V= rac{2}{3} imes rac{3}{5} imes rac{5}{2}$. Volume formula multiplies all three edge lengths.
$V= rac{2}{3} imes rac{3}{5} imes rac{5}{2}$. Volume formula multiplies all three edge lengths.
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Find the volume of a box with $l=\frac{4}{5}$ ft, $w=\frac{3}{2}$ ft, and $h=\frac{5}{6}$ ft.
Find the volume of a box with $l=\frac{4}{5}$ ft, $w=\frac{3}{2}$ ft, and $h=\frac{5}{6}$ ft.
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$1 , \mathrm{ft}^3$. Apply $V = lwh = \frac{4}{5} \times \frac{3}{2} \times \frac{5}{6} = 1$.
$1 , \mathrm{ft}^3$. Apply $V = lwh = \frac{4}{5} \times \frac{3}{2} \times \frac{5}{6} = 1$.
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