Volume of Composite Shapes 2

Years

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 4

1. Question
Find the volume of the figure
- $\text(Volume )=$ (3420) $\text(m)^3$
Hint

Help Video
Correct

Fantastic!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Volume of a Rectangular Prism

$\text(Volume )=\text(base) times \text(height) times$ $\text(depth)$

Labelling the given lengths

$\text(Smaller Rectangle)$

$\text(length)=9$

$\text(width)=8$

$\text(depth)=10$

$\text(Larger Rectangle)$

$\text(length)=9$

$\text(width)=30$

$\text(depth)=10$

We need to add volume of the smaller rectangle and the larger rectangle

First, find the area of the smaller rectangle

$\text(Area)$ $=$ $\text(length)$ $times$ $\text(width)$

$=$ $9$ $times$ $8$ $=$ $72 \text(m)^2$

Next, find the area of the larger rectangle

$\text(Area)$ $=$ $\text(length)$ $times$ $\text(width)$

$=$ $9$ $times$ $30$ $=$ $270 \text(m)^2$

Next, add the area of the smaller rectangle and the area of the larger rectangle

$=$ $72$ $+$ $270$ Plug in the two areas

$=$ $342 \text(m)^2$

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

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

$=$ $342$ $times$ $10$ Plug in the known lengths

$=$ $3420 \text(m)^3$

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

$\text(Volume)=3420 \text(m)^3$
Question 2 of 4

2. Question
Find the volume of the figure
- $\text(Volume )=$ (320) $\text(cm)^3$
Hint

Help Video
Correct

Excellent!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Volume of a Cube

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

Labelling the given lengths

$\text(Whole Figure)$

$\text(side)=7$

$\text(depth)=8$

$\text(Hollow Part)$

$\text(side)=3$

$\text(depth)=8$

We need to find the volume of the figure, not including its hollow part

First, find the area of the whole front face

$\text(Area)$ $=$ $\text(side)^2$

$=$ $7^2$ $=$ $49 \text(cm)^2$

Next, find the area of the inner shape on the front face

$\text(Area)$ $=$ $\text(side)^2$

$=$ $3^2$ $=$ $9 \text(cm)^2$

Finally, subtract the area of the inner shape from the whole shape

$=$ $49$ $-$ $9$ Plug in the two areas

$=$ $40 cm^2$

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

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

$=$ $40$ $times$ $8$ Plug in the known lengths

$=$ $320 \text(cm)^3$

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

$\text(Volume)=320 \text(cm)^3$
Question 3 of 4

3. Question
Find the volume of the figure

Round your answer to one decimal place
- $\text(Volume )=$ (2120.6) $\text(m)^3$
Hint

Help Video
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Volume of a Semicircle

$\text(Volume)=1/2 times pi times$ $\text(radius)^2$ $times$ $\text(height)$

Labelling the given lengths

$\text(Outer Semicircle)$

$\text(radius)=14$

$\text(height)=18$

$\text(Inner Semicircle)$

$\text(radius)$ $=14-3=$ $11$

$\text(height)=18$

We need to find the volume of the figure, not including its hollow part

Next, find the area of the Larger Semicircle

$pi ~~ 3.141592654$

$\text(Area)$ $=$ $1/2 times pi times$ $\text(radius)^2$

$=$ $1/2 times pi times$ $14^2$ $=$ $307.88 \text(m)^2$

Next, find the area of the Inner Semicircle

$\text(Area)$ $=$ $1/2 times pi times$ $\text(radius)^2$

$=$ $1/2 times pi times$ $11^2$ $=$ $190.07 \text(m)^2$

Now, subtract the area of the Inner Semicircle from the Outer Semicircle

$=$ $307.88$ $-$ $190.07$ Plug in the two areas

$=$ $117.81 \text(m)^2$

Finally, multiply the area by the height to find the volume

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

$=$ $117.81$ $times$ $18$ Plug in the known lengths

$=$ $2120.6 \text(m)^3$

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

$\text(Volume)=2120.6 \text(m)^3$
Question 4 of 4

4. Question
Find the volume of air inside the Cylinder

Round your answer to two decimal places
- $\text(Volume )=$ (268.08) $\text(cm)^3$
Hint

Help Video

Correct

Exceptional!

Incorrect

Volume of a Cylinder

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

Volume of a Sphere

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

Labelling the given lengths

$\text(Cylinder)$

$\text(radius)=?$

$\text(height)=16$

$\text(Spheres)$

$\text(radius)=?$

$\text(diameter)$ $=$ $16$ $divide2=$ $8$

We need subtract the volume of the two spheres from the volume of the cylinder

First, recall that the radius is equal to half of the diameter

$\text(radius)$ $=$ $1/2 times$ $8$

$\text(radius)$ $=$ $4$

Since the radius is the distance from the center to any end of the circle, we can use the same value as the radius of the cylinder

Next, use the formula to find the volume of the cylinder

$pi ~~ 3.141592654$

$\text(Area)$ $=$ $pi times$ $\text(radius)^2$ $times$ $\text(height)$

$=$ $pi times$ $4^2$ $times$ $16$ $=$ $804.25 \text(cm)^3$

Next, use the formula to find the volume of the spheres

$\text(Area)$ $=$ $4/3 times pi times$ $\text(radius)^3$

$=$ $4/3 times pi times$ $4^3$ $=$ $268.08 \text(cm)^3$

Finally, subtract the volume of the two spheres from the volume of the cylinder

$=$ $804.25$ $-($ $268.08$ $times 2)$ Plug in the two volumes

$=$ $268.08 \text(cm)^3$

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

$\text(Volume)=268.08 \text(cm)^3$

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Fantastic!

Volume of a Rectangular Prism

Labelling the given lengths

2. Question

Hint

Excellent!

Volume of a Cube

Labelling the given lengths

3. Question

Hint

Great Work!

Volume of a Semicircle

Labelling the given lengths

4. Question

Hint

Exceptional!

Volume of a Cylinder

Volume of a Sphere

Labelling the given lengths

Quizzes

$\text(Area)$	$=$	$\text(length)$ $times$ $\text(width)$
	$=$	$9$ $times$ $8$ $=$ $72 \text(m)^2$

$\text(Area)$	$=$	$\text(length)$ $times$ $\text(width)$
	$=$	$9$ $times$ $30$ $=$ $270 \text(m)^2$

	$=$	$72$ $+$ $270$	Plug in the two areas
	$=$	$342 \text(m)^2$

$\text(Volume)$	$=$	$\text(area)$ $times$ $\text(depth)$	Finding the volume
	$=$	$342$ $times$ $10$	Plug in the known lengths
	$=$	$3420 \text(m)^3$

$\text(Area)$	$=$	$\text(side)^2$
	$=$	$7^2$ $=$ $49 \text(cm)^2$

$\text(Area)$	$=$	$\text(side)^2$
	$=$	$3^2$ $=$ $9 \text(cm)^2$

$\text(Area)$	$=$	$1/2 times pi times$ $\text(radius)^2$

	$=$	$1/2 times pi times$ $14^2$ $=$ $307.88 \text(m)^2$

$\text(Area)$	$=$	$1/2 times pi times$ $\text(radius)^2$

	$=$	$1/2 times pi times$ $11^2$ $=$ $190.07 \text(m)^2$

	$=$	$307.88$ $-$ $190.07$	Plug in the two areas
	$=$	$117.81 \text(m)^2$

$\text(Volume)$	$=$	$\text(area)$ $times$ $\text(height)$	Finding the volume
	$=$	$117.81$ $times$ $18$	Plug in the known lengths
	$=$	$2120.6 \text(m)^3$

	$=$	$804.25$ $-($ $268.08$ $times 2)$	Plug in the two volumes
	$=$	$268.08 \text(cm)^3$

$\text(Area)$	$=$	$pi times$ $\text(radius)^2$ $times$ $\text(height)$
	$=$	$pi times$ $4^2$ $times$ $16$ $=$ $804.25 \text(cm)^3$

$\text(Area)$	$=$	$4/3 times pi times$ $\text(radius)^3$

	$=$	$4/3 times pi times$ $4^3$ $=$ $268.08 \text(cm)^3$