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

Answer:

384

Step-by-step explanation:

Answer 2

Answer:

The surface area without the base is 753.6 square inches

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

Step-by-step 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.

$C = 2\pi r\\\\24\pi = 2\pi r\\\\\frac{24\pi}{2\pi} = r \\12=r$

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