Page 258 - ABCTE Study Guide_Neat

Measuring Other Solids

Lesson Objective

Now we'll look at some other solids and how to calculate their volumes, surface areas, and other
characteristics. We'll also present some more questions and give you a chance to practice these skills.

Previously Covered

A cylinder is a solid whose bases are circles.

A cone is a solid with one circular base and one vertex.

A sphere is the set of all points in space that are equidistant from a given point called the center.

Cylinders

Recall that the surface area of a polyhedron is the sum of the areas of its polygonal faces. The surface
area of a cylinder is the sum of the areas of its faces, as well. Clearly, the two bases are circles, but the
other “face” is harder to see. This might help:

Since the radius of each circular base is r, then each circular base has area . When the side of the
cylinder is unwrapped, it becomes a rectangle with height h and width equal to the circumference of the
circle, or . Thus, the area of the rectangle is

So, the surface area of a cylinder is given by the formula , where r is the radius of the circular
bases and h is the height.

Question

What is the surface area of a cylinder with a base of radius 2 ft and a height of 3 ft? Give your answer in
terms of π and round your answer to the nearest square foot.

2
A 8π ft

2
B 12π ft