For a right circular cone, the ratio of the slant height to the length of the radius is 5 : 3. If the volume of the cone is 324𝜋 in3, find the lateral area (in square inches) of the cone.

Question

For a right circular cone, the ratio of the slant height to the length of the radius is 5 : 3. If the volume of the cone is 324𝜋 in3, find the lateral area (in square inches) of the cone.

( I keep reposting this because nobody will help me find the answer. I've looked in the book, got help from my mom. who's a math teacher. And she's having a hard time explaining it to me.

Answer 1

Draw and label a diagram!

The height of the cone is the long leg of a right triangle, a 3, 4, 5 triangle.

If the radius is 3x then the height is 4x

V = (1/3)πr²h

324π = (1/3)π(3x)²(4x)

324π = π12x³

27 = x³

3 = x

The radius is 9 and the height is 12.

L.A. = π r √(h² + r²)

Can you substitute values and answer?