Question

The base of a right circular cone has a radius of 4 inches and a slant height of 9 inches. If the radius and the slant height are multiplied by 6, by what factor is the surface area multiplied? A. 6 B. 36 C. 24 D. 54

Answer 1

Answer:

Correct option: B -> 36

Step-by-step explanation:

The surface area of a circular cone is given by the formula:

Surface area = pi * radius * (radius + slant height)

If the inicial radius is 4 in and the slant height is 9 in, we have:

Surface area = pi * 4 * (4 + 9) = 52pi in2

The radius and the slant height are multiplied by 6, so we have:

radius = 6 * 4 = 24 in

slant height = 6 * 9 = 54 in

So the new surface area is:

New surface area = pi * 24 * (24 + 54) = 1872pi in2

The factor of the surface areas is:

New surface area / Surface area = 1872pi / 52pi = 36

Correct option: B