Similar Solids Worksheet

**Page 3**

21.

If the ratio of surface areas of two similar solids is less than 1, then what is the similarity ratio of the solids?

a. | = 1 | ||

b. | > 1 | ||

c. | > 2 | ||

d. | < 1 |

[Ratio of surface areas < 1.]

Let the similarity ratio of these solids =

[Definition.]

[Find the square root of each side.]

Clearly,

Correct answer : (4)

22.

The similarity ratio of two similar solids is $k$, which is less than 1. The ratio of their surface areas is $l$ and the ratio of their volumes is $m$. Which of the following is correct?

a. | $l$ < $k$ < $m$ | ||

b. | $m$ < $l$ < $k$ | ||

c. | $l$ < $m$ < $k$ | ||

d. | $k$ < $l$ < $m$ |

[

Ratio of the surface area

[Definition.]

= (0.2)2 = 0.04

[Substitute 0.2 for

Ratio of volumes =

[Definition.]

= (0.2)3 = 0.008

[Substitute 0.2 for

So

Correct answer : (4)

23.

If the similarity ratio, ratio of surface areas and the ratio of volumes of two similar solids are $l$, $m$ and $n$ respectively, then which of the following is correct?

a. | $m$ = $\mathrm{ln}$ | ||

b. | $m$ ^{2} = $\mathrm{ln}$ | ||

c. | $l$ ^{2} = $\mathrm{mn}$ | ||

d. | $n$ ^{2} = $\mathrm{lm}$ |

[Given.]

Ratio of the surface area =

[Given.]

Ratio of the volume =

[Given.]

[Definition.]

So,

[Substitute

[Substituting

So,

Correct answer : (2)

24.

If the similarity ratio and the ratio of surface areas of two similar solids are $\frac{2}{x}$ and $\frac{x}{16}$ , then what is the ratio of the volumes of the solids?

a. | 4 : 1 | ||

b. | 2 : 1 | ||

c. | 1 : 4 | ||

d. | 1 : 2 |

[Given.]

Ratio of surface area of solids =

[Given.]

(

[Definition.]

[Cross - product property.]

[Find cube root on each side.]

So, the similarity ratio =

[Substitute 4 for

So, the ratio of the surface areas = (

[Definition.]

=

Correct answer : (3)

25.

The similarity ratio, ratio of surface areas and ratio of volumes of two similar solids are $\frac{2}{l}$ , $\frac{4}{m}$ and $\frac{8}{n}$ respectively. Which of the following is correct?

a. | $l$ ^{3} = $\mathrm{mn}$ | ||

b. | $l$ ^{5} = $\mathrm{mn}$ | ||

c. | $l$ ^{4} = $\mathrm{mn}$ | ||

d. | $l$ ^{2} = $\mathrm{mn}$ |

[Given.]

Ratio of surface areas of the solids =

[Given.]

Ratio of volumes of the solids =

[Given.]

[Definition.]

[Cross - product property.]

[Substitute

So,

Correct answer : (2)