Question

what is the surface area of this figure?
write an exact answer in terms of π.
square inches

Explanation:

Step1: Calculate the surface area of the large cylinders

The formula for the surface area of a cylinder is \(S = 2\pi r^2+ 2\pi rh\). For the large cylinders, \(r=\frac{8}{2}=4\) in and \(h = 2\) in.
The two - base area \(2\pi r^2=2\pi\times4^2 = 32\pi\), and the lateral surface area \(2\pi rh=2\pi\times4\times2=16\pi\).

Step2: Calculate the surface area of the small cylinder

For the small cylinder, \(r = 1\) in and \(h=6\) in. The lateral surface area \(2\pi rh=2\pi\times1\times6 = 12\pi\).

Step3: Combine the areas

The total surface area of the figure is the sum of the lateral surface area of the small cylinder and the surface areas of the two large cylinders.

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Answer:

\(108\pi\)