1. Find the volume of the sphere.

Round to the nearest tenth.

2. Find the volume of the hemisphere.

Round to the nearest tenth.

3. Find the volume of a sphere with

a diameter of 14.6 feet to the nearest tenth.

4. What is the radius of a sphere with a volume of 288 cubic meters?

• similar solids

• congruent solids

• Identify congruent or similar solids.

• State the properties of similar solids.

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Similar and Congruent Solids

A. Determine whether the pair of solids is similar, congruent, or neither.

Find the ratios between the corresponding parts of the square pyramids.

Simplify.

Substitution

Similar and Congruent Solids

Answer: The ratios of the measures are equal, so we can conclude that the pyramids are similar. Since the scale factor is not 1, the solids are not congruent.

Substitution

Simplify.

Simplify.

Substitution

Similar and Congruent Solids

B. Determine whether the pair of solids is similar, congruent, or neither.

Compare the ratios between the corresponding parts of the cones.

Similar and Congruent Solids

Answer: Since the ratios are not the same, the cones are neither similar nor congruent.

Simplify.

Substitution

Substitution

A. A

B. B

C. C

A. similar

B. congruent

C. neither

A. Determine whether the pair of solids is similar, congruent, or neither.

A. A

B. B

C. C

A. similar

B. congruent

C. neither

B. Determine whether the pair of solids is similar, congruent, or neither.

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Sports

A. Softballs and baseballs are both used to play a game with a bat. A softball has a diameter of 3.8 inches, while a baseball has a diameter of about 2.9 inches. Find the scale factor of the two balls.

Answer: The scale factor is about 1.3:1.

Write the ratio of the corresponding measures of the balls.

Substitution

Simplify.

Sports

B. Softballs and baseballs are both used to play a game with a bat. A softball has a diameter of 3.8 inches, while a baseball has a diameter of about 2.9 inches. Find the ratio of the surface areas of the two balls.

If the scale factor is a:b, then the ratio of the surface areas is

Sports

Answer: The ratio of the surface areas is about 1.7:1.

Simplify.

Theorem 13.1

Sports

C. Softballs and baseballs are both used to play a game with a bat. A softball has a diameter of 3.8 inches, while a baseball has a diameter of about 2.9 inches. Find the ratio of the volumes of the two balls.

If the scale factor is a : b, then the ratio of the volumes is

Sports

Answer: The ratio of the volumes of the two balls is about 2.2:1.

Theorem 13.1

Simplify.

1. A

2. B

3. C

4. D

A. 18:7

B. 9:7

C. 9:3.5

D. 2:1

A. Two sizes of balloons are being used for decorating at a party. When fully inflated, the balloons are spheres. The first balloon has a diameter of 18 inches while the second balloon has a radius of 7 inches. Find the scale factor of the two balloons.

1. A

2. B

3. C

4. D

A. 18:7

B. 9:7

C. 18:14

D. 81:49

B. Two sizes of balloons are being used for decorating at a party. When fully inflated, the balloons are spheres. The first balloon has a diameter of 18 inches while the second balloon has a radius of 7 inches. Find the ratio of the surface areas of the two balloons.

1. A

2. B

3. C

4. D

A. 9:7

B. 81:49

C. 729:343

D. 162:98

C. Two sizes of balloons are being used for decorating at a party. When fully inflated, the balloons are spheres. The first balloon has a diameter of 18 inches while the second balloon has a radius of 7 inches. Find the ratio of the volumes of the two balloons.