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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Volumes of Prisms and Cylinders

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Exercise 49 Page 838

Use the formula for a volume of a cylinder.

F

Practice makes perfect

A cylindrical tank can be modeled by the following cylinder. Its height is half the length of its radius. Let r denote the radius of the tank. This tells us that h= r2 is its height.

The volume of the cylinder is 1 122 360 cubic feet. Let's use the formula for the volume of a cylinder to find the value of r.

V=π r^2h

V= 1 122 360, h= r/2

1 122 360=π r^2* r/2

▼

Solve for r

MoveLeftFacToNum

a*b/c= a* b/c

1 122 360=π r^2* r/2

Multiply

1 122 360=π r^3/2

LHS * 2=RHS* 2

2 244 720=π r^3

Rearrange equation

π r^3=2 244 720

π ≈ 3.1416

3.1416r^3≈ 2 244 720

.LHS /3.1416.=.RHS /3.1416.

r^3≈2 244 720/3.1416

Calculate quotient & Use a calculator

r^3≈ 714 514.896868

sqrt(LHS)=sqrt(RHS)

r≈sqrt(714 514.896868)

Calculate root & Use a calculator

r≈ 83.399912

Round to 1 decimal place(s)

r≈ 83.4

Finally, we find that the radius of the tank is about 83.4 feet. That answer corresponds to option F.

Subchapter links

Exercises p.834-838