Question

Question A: A right cone has a radius of 3 ft and slant height 7 ft. The radius and slant height are both doubled. Which of the following correctly describes the effect on the surface area?

1. The surface area is multiplied by 4.
2. The surface area is multiplied by 1/2.
3. The surface area is multiplied by 1/4.
4. The surface area is multiplied by 2.

Question B: A right cone has a radius of 2 ft and slant height 5 ft. The radius and slant height are both multiplied by 1/4. Which of the following correctly describes the effect on the surface area?

1. The surface area is multiplied by 16.
2. The surface area is multiplied by 8.
3. The surface area is multiplied by 1/16.
4. The surface area is multiplied by 1/8.

Answer 1

Question A: 1. The surface area is multiplied by 4

Question B: 3. The surface area is multiplied by 1/16

Explanation:

The effect of scaling the linear dimensions by some factor is to scale the area by the square of that factor.

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Question A: 2^2 = 4. Area is multiplied by 4.

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Question B: (1/4)^2 = 1/16. Area is multiplied by 1/16.