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Areas and Volumes of Similar Solids – Practice 01

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For 1-6, the scale factor between the two similar figures is given. The surface area and volume of the smaller figure is given. Find the surface area and volume of the larger figure. For 6-9, two similar figures are given. Find the corresponding part of the larger figure.

1. $ScaleFactor=2:5$
$SA=72km^2$
$V=56km^3$

$SA=900km^2$ $V=140km^3$

$SA=450km^2$ $V=875km^3$

$SA=2250km^2$ $V=875km^3$

$SA=450km^2$ $V=2250km^3$

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Question 1 of 10

2. $ScaleFactor=2:3$
$SA=720km^2$
$V=4536km^3$

$SA=9720km^2$ $V=6804km^3$

$SA=14580km^2$ $V=15309km^3$

$SA=1620km^2$ $V=14580km^3$

$SA=1620km^2$ $V=15309km^3$

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Question 2 of 10

3. $ScaleFactor=1:2$
$SA=208km^2$
$V=1088km^3$

$SA=832km^2$ $V=6656km^3$

$SA=832km^2$ $V=1088km^3$

$SA=832km^2$ $V=8704km^3$

$SA=104km^2$ $V=136km^3$

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Question 3 of 10

4. $ScaleFactor=2:3$
$SA=320km^2$
$V=1856km^3$

$SA=720km^2$ $V=6264km^3$

$SA=2880km^2$ $V=2784km^3$

$SA=720km^2$ $V=4320km^3$

$SA=720km^2$ $V=1044km^3$

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Question 4 of 10

5. $ScaleFactor=5:7$
$SA=225km^2$
$V=1250km^3$

$SA=2205km^2$ $V=1750km^3$

$SA=441km^2$ $V=3087km^3$

$SA=441km^2$ $V=3430km^3$

$SA=63km^2$ $V=70km^3$

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Question 5 of 10

6. $ScaleFactor=1:2$
$SA=144km^2$
$V=1408km^3$

$SA=576km^2$ $V=1408km^3$

$SA=2304km^2$ $V=2816km^3$

$SA=4608km^2$ $V=11264km^3$

$SA=576km^2$ $V=11264km^3$

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Question 6 of 10

7.

Which of the following is the value of $x$ ?

$5in$

$4in$

$6in$

$2in$

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Question 7 of 10

8.

What is the ratio of the smaller shape's volume compared to the larger shape's volume?

$1:27$

$1:9$

$1:3$

$1:18$

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Question 8 of 10

9.

The dimensions of the larger shape are four times greater than the smaller shape. What is its surface area?

$400m^2$

$200m^2$

$6400m^2$

$1600m^2$

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Question 9 of 10

10. The side length of a solid figure is $a$ $cm$ . The side length of a similar figure is $b$ $cm$ . What is the ratio of their volumes?

$\dfrac{a^2}{b^2}$

$\dfrac{a}{b}$

$ab$

$\dfrac{a^3}{b^3}$

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Question 10 of 10

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