Question

SOMEONE PLEASE ANSWER CORRECTLY!!!

A cone has a radius of 2 inches and a slant height of 12 inches.

What is the exact surface area of a similar cone whose radius is 6 inches?

Enter your answer in the box.

Surface area of similar cone =
in²

Answer 1

answer: 252pi in squared or 791.68 in squared

hey! so first we know that the cones are similar, which means their scale factor is 1/3 (because the radii are 2/6 and we simplified it)

then, we can find the height of the similar coke by using that scale factor and plugging them in:
1/3 = 12/slant height of similar cone
slant height = 36 in

the formula for the surface area of a cone is pi(radius)squared + pi(radius)(slant height)

plug the values we found and you get that the area of the similar cone is 252pi or 791.68 insquared!

Answer 2

First, we can find the height of the original cone using the Pythagorean theorem:

height = sqrt(slant height^2 - radius^2) = sqrt(12^2 - 2^2) = sqrt(142) inches

The surface area of the original cone is:

SA = πr(r + √(r^2 + h^2)) = π(2)(2 + √(2^2 + (sqrt(142))^2)) ≈ 46.63 in²

The ratio of the radii of the two cones is 6/2 = 3, so the ratio of their surface areas is 3^2 = 9.

Therefore, the surface area of the similar cone is:

SA = 9 × 46.63 = 419.67 in² (rounded to two decimal places)

So the exact surface area of the similar cone with a radius of 6 inches is 419.67 in².

Explanation: