McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
2. Surface Areas of Prisms and Cylinders
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Exercise 18 Page 818

Use the formula for the surface area of a cylinder.

Lateral Area: About 1000.6 square centimeters
Surface Area: About 1266.1 square centimeters

Practice makes perfect

A cereal container can be modeled by the following cylinder with a height of h= 24.5 centimeters and a diameter of 13 centimeters. This tells us that the radius of the cylinder is r= 132= 6.5 centimeters.

We are asked to find the lateral area and the surface area of the container and round it to the nearest tenth if necessary. First, let's find the lateral area. The lateral area is given by the equation L=2π r h. Now, let's substitute the known values into the equation.
L=2π r h
Substitute values and evaluate
L=2π( 6.5)( 24.5)
L=318.5π
L=1000.597260...
L≈ 1000.6
Therefore, the lateral area of the container is about 1000.6 square centimeters. Now, to find the surface area of the cylinder S, we should add areas of two bases to the lateral area. Since each base is a circle, let's use the formula for the area of a circle.
S=L+2*Area of Base
S=L+2π r^2
S=1000.6+2π( 6.5)^2
Evaluate
S=1000.6+84.5π
S=1266.064579...
S≈ 1266.1
We found that the surface area is about 1266.1 square centimeters.