Volume of Shapes 1

Years

Year 8

Surface Area and Volume

Volume of Shapes

Volume of Shapes 1

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Question 1 of 7

1. Question
Find the volume of the Rectangular Prism

The given measurements are in units
- $\text(Volume )=$ (48) $\text(units)^3$
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Volume of a Rectangular Prism

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

In a regular cube, all sides are equal

Labelling the given lengths

$\text(side)=4$

$\text(depth)=3$

First, find the area of the front face

$\text(Area)$ $=$ $\text(side)$ $times$ $\text(side)$ Area of a Square

$=$ $4$ $times$ $4$ Plug in the known lengths

$=$ $16 \text(units)^2$

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

$\text(Volume)$ $=$ $\text(area)$ $times$ $\text(depth)$ Finding the volume

$=$ $16$ $times$ $3$ Plug in the known lengths

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

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

$\text(Volume)=48 \text(units)^3$
Question 2 of 7

2. Question
What is the volume of this cube?
- Volume $=$ (729) $m^3$
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Volume of a Cube

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

Labelling the given lengths

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

Use the formula to find the volume

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

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

$=$ $729$ Simplify

$=$ $729 \ m^3$

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

Volume $=729 \ m^3$
Question 3 of 7

3. Question
Find the volume of the Prism
- $\text(Volume )=$ (696) $\text(cm)^3$
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Volume of a Triangular Prism

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

Labelling the given lengths

$\text(base)=8$

$\text(height)=6$

$\text(depth)=29$

First, find the area of the front face

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

$=$ $1/2 times$ $8$ $times$ $6$ Plug in the known lengths

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

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

$\text(Volume)$ $=$ $\text(area)$ $times$ $\text(depth)$ Finding the volume

$=$ $24$ $times$ $29$ Plug in the known lengths

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

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

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

Question 4 of 7

What is the volume of this Rectangular Prism?

Volume $=$ (336) $mm^3$

Question 5 of 7

5. Question
What is the volume of this cube?
- Volume $=$ (2,197) $cm^3$
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Volume of a Cube

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

Labelling the given lengths

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

Use the formula to find the volume

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

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

$=$ $2,197$ Simplify

$=$ $2,197 \ cm^3$

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

Volume $=2,197 \ cm^3$

Question 6 of 7

Find the volume of the Cylinder

Round your answer to

$2$ decimal places

Use

$pi=3.141592654$

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

Using	Answer
$pi=3.141592654$	$254.47 m^3$
$pi=3.14$	$254.34 m^3$
$pi=(22)/(7)$	$254.57 m^3$

Question 7 of 7

Find the volume of the Sphere

Round your answer to

$1$ decimal place

Use

$pi=3.141592654$

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

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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

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

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

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

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

	$=$	$729$	Simplify

	$=$	$729 \ m^3$

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

	$=$	$1/2 times$ $8$ $times$ $6$	Plug in the known lengths

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

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

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

	$=$	$336$
	$=$	$336 \ mm^3$

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

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

	$=$	$2,197$	Simplify

	$=$	$2,197 \ cm^3$

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

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

	$=$	$4/3 times 3.141592654 times$ $24^3$	Plug in the known lengths

	$=$	$4/3 times 3.141592654 times 13824$	Simplify

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

Using	Answer
$pi=3.141592654$	$57905.8 cm^3$
$pi=3.14$	$57876.5 cm^3$
$pi=(22)/(7)$	$57929.1 cm^3$

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

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