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

Answer:

$136\pi in^2$

Step-by-step 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 $136\pi in^2$