Question

A cone has a slant height of 10 inches and a diameter of 12 inches. What is the surface area of the cone?

Answer 1

Answer:
`S=96\pi` inches^2, or approximately 301.59 inches^2.

The surface area of the cone is 96(pi) square inches.

Explanation:

The surface area of a cone is found using the formula:
`S=\pi √(r^2+h^2)`, where r is the radius and h is the height. With slant height, this is:
`S=\pi r^2 +\pi rl`

The diameter is twice the length of the radius, so divide the diameter of 12 inches by 2, and r = 6 inches.

We are given the slant height: 10 inches.

Plug these into the surface area equation:

`S=\pi (6)^2+\pi (6)(10)`

Simplify:

`S=\pi (36)+\pi (60)\\S=36\pi+60\pi`

Add like terms and:

`S=96\pi` square inches