Question

A right cone has radius 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?

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

Answer 1

When the radius and slant height of a right cone are both doubled, the surface area is multiplied by 2.

Step-by-step explanation:

To determine the effect on the surface area of a right cone when the radius and slant height are both doubled, we need to calculate the surface area of the original cone and the surface area of the new cone and compare them. The formula for the surface area of a cone is given by A = πr(r + s), where r is the radius and s is the slant height.

1. For the original cone with a radius of 3 ft and slant height of 7 ft, the surface area is A = π(3)(3 + 7) = 10π ft².
2. For the new cone with a doubled radius of 6 ft and doubled slant height of 14 ft, the surface area is A = π(6)(6 + 14) = 20π ft².

Comparing the two surface areas, we can see that the surface area of the new cone is 2 times the surface area of the original cone. Therefore, the correct answer is The surface area is multiplied by 2.