Volume of Shapes 1

Question 1 of 7

Find the volume of the Rectangular Prism

The given measurements are in units

$Volume =$ $\text(Volume )=$ (48) ${units}^{3}$ $\text(units)^3$

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Volume of a Rectangular Prism

Volume =

$\text(Volume )=$ $side$ $\text(side)$

\times

$times$ $side$ $\text(side)$

\times

$times$ $depth$ $\text(depth)$

In a regular cube, all sides are equal

Labelling the given lengths

side = 4

$\text(side)=4$

depth = 3

$\text(depth)=3$

First, find the area of the front face

$Area$ $\text(Area)$	$=$ $=$	$side$ $\text(side)$ $\times$ $times$ $side$ $\text(side)$	Area of a Square
	$=$ $=$	$4$ $4$ $\times$ $times$ $4$ $4$	Plug in the known lengths
	$=$ $=$	$16 {units}^{2}$ $16 \text(units)^2$

Next, multiply the area by the depth to find the volume

$Volume$ $\text(Volume)$	$=$ $=$	$area$ $\text(area)$ $\times$ $times$ $depth$ $\text(depth)$	Finding the volume
	$=$ $=$	$16$ $16$ $\times$ $times$ $3$ $3$	Plug in the known lengths
	$=$ $=$	$48 {units}^{3}$ $48 \text(units)^3$

The given measurements are in units, so the volume is measured as units cubed

Volume = 48 {units}^{3}

$\text(Volume)=48 \text(units)^3$

Question 2 of 7

What is the volume of this cube?

Volume $=$ $=$ (729) $m^{3}$ $m^3$

Incorrect

Volume of a Cube

V = s^{3}

$V=color(darkviolet)(s)^3$

Labelling the given lengths

side = 9

$color(darkviolet)(\text(side)=9)$

Use the formula to find the volume

$V$ $V$	$=$ $=$	$s^{3}$ $color(darkviolet)(s)^3$	Volume of a cube formula

	$=$ $=$	$9^{3}$ $color(darkviolet)(9)^3$	Plug in the known lengths

	$=$ $=$	$729$ $729$	Simplify

	$=$ $=$	$729 m^{3}$ $729 \ m^3$

The given measurements are in metres, so the volume is measured as metres cubed

Volume

= 729 m^{3}

$=729 \ m^3$

Question 3 of 7

Find the volume of the Prism

$Volume =$ $\text(Volume )=$ (696) ${cm}^{3}$ $\text(cm)^3$

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Volume of a Triangular Prism

Volume = \frac{1}{2} \times

$\text(Volume )=1/2 times$ $base$ $\text(base)$

\times

$times$ $height$ $\text(height)$

\times

$times$ $depth$ $\text(depth)$

Labelling the given lengths

base = 8

$\text(base)=8$

height = 6

$\text(height)=6$

depth = 29

$\text(depth)=29$

First, find the area of the front face

$Area$ $\text(Area)$	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $base$ $\text(base)$ $\times$ $times$ $height$ $\text(height)$	Area of a Triangle

	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $8$ $8$ $\times$ $times$ $6$ $6$	Plug in the known lengths

	$=$ $=$	$24 {cm}^{2}$ $24 \text(cm)^2$

Next, multiply the area by the depth to find the volume

$Volume$ $\text(Volume)$	$=$ $=$	$area$ $\text(area)$ $\times$ $times$ $depth$ $\text(depth)$	Finding the volume
	$=$ $=$	$24$ $24$ $\times$ $times$ $29$ $29$	Plug in the known lengths
	$=$ $=$	$696 {cm}^{3}$ $696 \text(cm)^3$

The given measurements are in centimetres, so the volume is measured as centimetres cubed

Volume = 696 {cm}^{3}

$\text(Volume)=696 \text(cm)^3$

Question 4 of 7

What is the volume of this Rectangular Prism?

Volume $=$ $=$ (336) $m m^{3}$ $mm^3$

Incorrect

Volume of a Rectangular Prism

V = height \times width \times depth

$V=color(royalblue)(\text(height)) xx color(darkviolet)(\text(width))xx color(green)(\text(depth))$

Labelling the given lengths

height = 12

$color(royalblue)(\text(height)=12)$

width = 7

$color(darkviolet)(\text(width)=7)$

depth = 4

$color(green)(\text(depth)=4)$

Use the formula to find the volume

$V$ $V$	$=$ $=$	$height \times width \times depth$ $color(royalblue)(\text(height)) xx color(darkviolet)(\text(width))xx color(green)(\text(depth))$	Volume of a Rectangular Prism formula

	$=$ $=$	$12 \times 7 \times 4$ $color(royalblue)(\text(12)) xx color(darkviolet)(\text(7))xx color(green)(\text(4))$	Plug in the known lengths

	$=$ $=$	$336$ $336$
	$=$ $=$	$336 m m^{3}$ $336 \ mm^3$

The given measurements are in millimetres, so the volume is measured as millimetres cubed

Volume

= 336 m m^{3}

$=336 \ mm^3$

Question 5 of 7

What is the volume of this cube?

Volume $=$ $=$ (2,197) $c m^{3}$ $cm^3$

Incorrect

Volume of a Cube

V = s^{3}

$V=color(darkviolet)(s)^3$

Labelling the given lengths

side = 13

$color(darkviolet)(\text(side)=13)$

Use the formula to find the volume

$V$ $V$	$=$ $=$	$s^{3}$ $color(darkviolet)(s)^3$	Volume of a cube formula

	$=$ $=$	$13^{3}$ $color(darkviolet)(13)^3$	Plug in the known lengths

	$=$ $=$	$2, 197$ $2,197$	Simplify

	$=$ $=$	$2, 197 c m^{3}$ $2,197 \ cm^3$

The given measurements are in centimetres, so the volume is measured as centimetres cubed

Volume

= 2, 197 c m^{3}

$=2,197 \ cm^3$

Question 6 of 7

Find the volume of the Cylinder

Round your answer to

2

$2$ decimal places

Use

π = 3.141592654

$pi=3.141592654$

$Volume =$ $\text(Volume )=$ (254.47, 254.34, 254.57) $m^{3}$ $\text(m)^3$

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Volume of a Cylinder

Volume = π \times

$\text(Volume)=pi times$ ${radius}^{2}$ $\text(radius)^2$

\times

$times$ $height$ $\text(height)$

Labelling the given lengths

radius = 3

$\text(radius)=3$

height = 9

$\text(height)=9$

Use the formula to find the volume

Use

π = 3.141592654

$pi=3.141592654$ See

π

$pi$ explained

$Volume$ $\text(Volume)$	$=$ $=$	$π \times$ $pi times$ ${radius}^{2}$ $\text(radius)^2$ $\times$ $times$ $height$ $\text(height)$	Volume of a Cylinder formula
	$=$ $=$	$3.141592654 \times$ $3.141592654 times$ $3^{2}$ $3^2$ $\times$ $times$ $9$ $9$	Plug in the known lengths
	$=$ $=$	$3.141592654 \times 9 \times 9$ $3.141592654 times 9 times 9$	Simplify
	$=$ $=$	$254.46900$ $254.46900$
	$=$ $=$	$254.47 m^{3}$ $254.47 \text(m)^3$	Rounded to $2$ $2$ decimal places

The given measurements are in metres, so the volume is measured as metres cubed

Volume = 254.47 m^{3}

$\text(Volume)=254.47 \text(m)^3$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.141592654

$pi=3.141592654$ .

Using	Answer
$π = 3.141592654$ $pi=3.141592654$	$254.47 m^{3}$ $254.47 m^3$
$π = 3.14$ $pi=3.14$	$254.34 m^{3}$ $254.34 m^3$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$254.57 m^{3}$ $254.57 m^3$

Question 7 of 7

Find the volume of the Sphere

Round your answer to

1

$1$ decimal place

Use

π = 3.141592654

$pi=3.141592654$

$Volume =$ $\text(Volume )=$ (57905.8, 57876.5, 57929.1) ${cm}^{3}$ $\text(cm)^3$

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Volume of a Sphere

Volume = \frac{4}{3} \times π \times

$\text(Volume)=4/3 times pi times$ ${radius}^{3}$ $\text(radius)^3$

Labelling the given lengths

radius = ?

$\text(radius)=?$

diameter = 48

$\text(diameter)=48$

Recall that the radius is equal to half of the diameter

$radius$ $\text(radius)$	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $48$ $48$

$radius$ $\text(radius)$	$=$ $=$	$24$ $24$

Now we can use the formula to find the volume

Use

π = 3.141592654

$pi=3.141592654$ See

π

$pi$ explained

$Volume$ $\text(Volume)$	$=$ $=$	$\frac{4}{3} \times π \times$ $4/3 times pi times$ ${radius}^{3}$ $\text(radius)^3$	Volume of a Sphere formula

	$=$ $=$	$\frac{4}{3} \times 3.141592654 \times$ $4/3 times 3.141592654 times$ $24^{3}$ $24^3$	Plug in the known lengths

	$=$ $=$	$\frac{4}{3} \times 3.141592654 \times 13824$ $4/3 times 3.141592654 times 13824$	Simplify

	$=$ $=$	$57905.83579$ $57905.83579$
	$=$ $=$	$57905.8 {cm}^{3}$ $57905.8 \text(cm)^3$	Rounded to one decimal place

The given measurements are in centimetres, so the volume is measured as centimetres cubed

Volume = 57905.8 {cm}^{3}

$\text(Volume)=57905.8 \text(cm)^3$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.141592654

$pi=3.141592654$ .

Using	Answer
$π = 3.141592654$ $pi=3.141592654$	$57905.8 c m^{3}$ $57905.8 cm^3$
$π = 3.14$ $pi=3.14$	$57876.5 c m^{3}$ $57876.5 cm^3$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$57929.1 c m^{3}$ $57929.1 cm^3$

Volume of Shapes 1

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Quiz summary

Information

1. Question

Hint

Great Work!

Volume of a Rectangular Prism

Labelling the given lengths

2. Question

Keep Going!

Volume of a Cube

Labelling the given lengths

3. Question

Hint

Excellent!

Volume of a Triangular Prism

Labelling the given lengths

4. Question

Keep Going!

Volume of a Rectangular Prism

Labelling the given lengths

5. Question

Keep Going!

Volume of a Cube

Labelling the given lengths

6. Question

Hint

Nice Job!

Volume of a Cylinder

Labelling the given lengths

7. Question

Hint

Well Done!

Volume of a Sphere

Labelling the given lengths

Quizzes