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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

2. Surface Areas of Prisms and Cylinders

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Exercise 39 Page 820

Use the formula for the surface area of a cylinder.

Only Derek is correct. See solution.

Practice makes perfect

Montell and Derek are finding the surface area of a cylinder with a height of h= 5 centimeters and a radius of r= 6 centimeters.

We are asked to check if either of them is correct. First we will solve it correctly, and then we will analyze their solutions.

Correct Solution

Let's use the formula for the surface area of a cylinder.

S=2π r^2+2π r h

r= 6, h= 5

S=2π( 6)^2+2π( 6)( 5)

▼

Evaluate right-hand side

Calculate power and product

S=72π+60π

Add terms

S=132π

Therefore, the surface area of the given cylinder is 132π square centimeters.

Derek's Solution

As we can see, Derek's solution is almost the same as ours. This tells us that his solution is correct.

Montell's Solution

Montell gets an answer S=66π cm^2. It is different from the correct answer. Therefore, he is not correct. However, let's find where he made a mistake.

Montell
S&=π( 6)^2+π( 6)( 5) &=36π+30π &=66π cm^2

It appears that Montell used the formula S=π r^2+π rh to find the surface area of the cylinder. But, the correct formula is S=2π r^2+2π rh.

Subchapter links

Exercises p.817-821