Question

The circumference of the base of a cone is 24pi inches. The slant height of the cone is 20 inches what is the surface area of the cone express the answer in terms of pi

Answer 1

384

Explanation:

Answer 2

The surface area without the base is 753.6 square inches

The surface area with the base is 1,205.75 square inches

Explanation:

The lateral surface area of a right cone using the slant height is
`\pi r l` where r is the radius and l is the slant height. We know the slant height is 20 inches. To find the radius, use the circumference given and solve for r.

`C = 2\pi r\\\\24\pi = 2\pi r\\\\(24\pi)/(2\pi) = r \\12=r`

Now find the lateral surface area
`\pi (20)(12) = 753.6`

This is the surface area without the base. Add the lateral surface area to the area of the base
`A=\pi r^2\\A =\pi (12)^2\\A = 452.16`

The total surface area is 452.16 + 753.6 = 1, 205.76