Question

A tin man has a head that is a cylinder with a cone on top. The height of the cylinder is 12 inches and the slant height of the cone is 6 inches. The radius of both the cylinder and the cone is 4 inches. What is the surface area of the tin man's head in terms of pi?

A) 136π in²
B) 152π in²
C) 168π in²
D) 172π in²

I already figured out the surface area of the cylinder (128π in).. I just don't know how to include the cone into the equation. I'm stumped.. Please help

Answer 1

the answer would be C

Answer 2

`136\pi in^2`

Explanation:

Height of cylinder = 12 inches

Radius of cylinder = 4 inches

Since we are given that A tin man has a head that is a cylinder with a cone on top.

So, Surface area of cylinder = Curved surface area of cylinder + Area of one base

=
`2 \pi r h +\pi r^2`

=
`2 \pi (4)(12)+\pi(4)^2`

=
`96 \pi +16\pi`

=
`112\pi`

Cone is joined on the top of the cylinder

So, we are required to find the lateral surface area of cone .

Slant height of cone = 6 inches

Radius of cone = 4 inches

So, Lateral surface area of cone =
`\pi r l`

=
`\pi (4) (6)`

=
`24\pi`

Thus the total surface area =
`112\pi + 24\pi`

=
`136\pi in^2`

Hence the surface area of the tin man's head in terms of pi is
`136\pi in^2`