Similar Solids Worksheet

**Page 1**

1.

Two similar cylinders have heights 3 cm and 2 cm. What is the similarity ratio?.

a. | 3 : 2 | ||

b. | 4 : 3 | ||

c. | 3 : 4 | ||

d. | 2 : 3 |

[Given.]

The ratio of corresponding dimensions of two similar solids is the similarity ratio.

[Definition.]

Similarity ratio =

[Substitute 3 for

Correct answer : (1)

2.

Two similar cones have heights 8 cm and 4 cm. What is the ratio of their surface areas?

a. | 2 : 1 | ||

b. | 6 : 1 | ||

c. | 8 : 1 | ||

d. | 4 : 1 |

[Given.]

The ratio of corresponding dimensions of two similar solids is the similarity ratio.

[Definition.]

Similarity ratio =

=

[Substitute 8 for

The ratio of their corresponding surface area is

[Theorem.]

=

[Substitute and simplify.]

Correct answer : (4)

3.

The radii of two spheres are 3 cm and 2 cm. Find the ratio of their volumes approximately.

a. | 9 : 4 | ||

b. | 27 : 8 | ||

c. | 3 : 2 | ||

d. | 2 : 3 |

[Given.]

Similarity ratio =

[Formula.]

=

[Substitute 3 for

The ratio of Volumes of the solids is

[Formula.]

Correct answer : (2)

4.

The ratio of areas of two similar solids is 9 : 1. What is the similarity ratio of the solids?

a. | 3 : 1 | ||

b. | 9 : 1 | ||

c. | 1 : 3 | ||

d. | 1 : 9 |

[The ratio of the areas is

[Find the square root of each side.]

So, the similarity ratio of the two solids is

Correct answer : (1)

5.

The ratio of volumes of two similar solids is 27 : 8 . What is the similarity ratio of the solids?

a. | 3 : 2 | ||

b. | 9 : 4 | ||

c. | 4 : 9 | ||

d. | 2 : 3 |

[The ratios of the volumes is

[Find the cube root of each side.]

So, the similarity ratio of the two solids is

Correct answer : (1)

6.

The ratio of the base areas of two similar cylinders is 1 : 4 . What is the ratio of the volumes of the solids?

a. | 1 : 2 | ||

b. | 8 : 1 | ||

c. | 1 : 4 | ||

d. | 1 : 8 |

[The ratios of the base areas is

[Find the square root on each side.]

So,

[Substitute

The ratio of volumes of the two solids is

Correct answer : (4)

7.

The ratio of volume of two similar cones is 1 : 512 . Find the ratio of the base areas of the two solids.

a. | 64 : 1 | ||

b. | 1 : 64 | ||

c. | 1 : 8 | ||

d. | 8 : 1 |

[The ratios of the volume is

[Find the cube root of each side.]

So,

[Substitute (

The ratio of base areas of the two solids is

Correct answer : (2)

8.

The ratio of the volumes of two similar solids is 8 : 27. What is the volume of the smallest one?

a. | 3 cubic units | ||

b. | 2 cubic units | ||

c. | 8 cubic units | ||

d. | cannot be determined |

[Given.]

[The ratio of the volume is

Without knowing the volume of the larger solid

Correct answer : (4)

9.

The heights of two similar solids are 4 cm and $x$ cm. The similarity ratio of these two similar solids is 2 : 3. Find the value of $x$.

a. | 4 | ||

b. | 7 | ||

c. | 6 | ||

d. | 8 |

[Similarity ratio is

[Substitute 4for

[Cross product property.]

Correct answer : (3)

10.

The surface area of two similar spheres are 144$\pi $ cm^{2} and 16$\pi $ cm^{2} . The volume of the smaller solid is $\frac{32}{3}$$\pi $ cm^{3}. What is the volume of the larger sphere?

a. | 144 $\pi $ cm ^{3} | ||

b. | 288 $\pi $ cm ^{3} | ||

c. | 288 cm ^{3} | ||

d. | 144 cm ^{3} |

[Divide numerator and denominator by the common factor 16

[Find the square root of each side.]

Let

[Substitute

[Cross product property.]

The volume of the larger sphere is 288

Correct answer : (2)