Question

I give thanks :) This is worth 16 points

Find the surface area in square inches of the composite figure. Round your answer to the nearest hundredth.
To clarify, there is a hole where the bottom of the small cylinder would be, and that hole is also present in the top of the big cylinder. In other words, there is only one base in the small cylinder, and the top base of the big cylinder has a hole cut in it.
Show all of your work and label your answer to earn credit.

Answer 1

surface area is defined as the sum of all the areas covers the object so here we have 2 cylinders and the
Area of a cylinder = side area + area of the circle 
side area = perimeter * height = 2*pi* r *h
area of the circle = pi * r^2 
for the cylinder, we have 2 area circle and 1 side area 
so surface area = 2 *pi * r*h + 2 pi* r^2 
so for the first cylinder 
A1 = 2*pi*r*h +2 pi * r^2 = (2*pi * 2 *2) +( 2 *pi * 2^2 ) = 16pi inch^2 
A2 = 2*pi*r*h + 2pi *r^2 = ( 2 * pi * 1.25*3)+( 2*pi *(1.25)^2) = 85/8 pi inch^2 
A= A1 +A2 
A = 16pi + 85/8 pi = 83.645 inch^2