Question

Please help!!

What are the lateral area and the surface area of the cone shown below? Round the answers to the nearest tenth. The figure is not drawn to scale.

A. LA = 615.8 ft2; SA = 1,803.3 ft2
B. LA = 615.8 ft2; SA = 3,166.7 ft2
C. LA = 1,187.5 ft2; SA = 1,803.3 ft2
D. LA = 1,187.5 ft2; SA = 3,166.7 ft2

Answer 1

Given:

The radius of the cone = 14 ft

The slant height of the cone = 27 ft

To find the lateral surface area and the total surface area of the given cone.

Formula

The lateral surface area of the cone is

`LSA = \pi rl` and

The total surface area of the cone is

`TSA = \pi r^(2) + \pi r l`

where,

r be the radius and

l be the slant height of the cone.

Now

Taking r = 14 and l = 27 we get

`LSA = \pi (14)(27)` sq ft

or,
`LSA = 1187.5` sq ft

Again,

`TSA = \pi(14^2)+\pi (14)(27)` sq ft

or,
`TSA = 1803.3` sq ft

Hence,

The lateral surface area of the cone is 1187.5 sq ft and the total surface area of the cone is 1803.3 sq ft. Option C.