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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 33 Page 836

Use the formulas for the surface area and volume of a cylinder.

678.6 in^3

Practice makes perfect

The volume of a cylinder with the radius r and height h can be calculated by the following formula. V=π r^2 h We are given the height h = 6in. We know the surface area S=144πin^2, so we can find the radius using the following formula. S=2π rh+2π r^2 In this formula, r is the radius of the base and h is the height of the cylinder. Substituting S with 144π and h with 6 into the formula, we can solve for r. Let's do it!

S=2π rh+2π r^2

S= 144π, h= 6

144π=2π r( 6)+2π r^2

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Solve for r

.LHS /2π.=.RHS /2π.

72=6r+r^2

LHS-72=RHS-72

0=6r+r^2-72

Rearrange equation

r^2+6r-72=0

Rewrite 6r as 12r-6r

r^2+12r-6r-72=0

Factor out r

r(r+12) -6r-72=0

Factor out (-6)

r(r+12)-6(r+12) = 0

Factor out r+12

(r-6)(r+12) = 0

Use the Zero Product Property

r = 6orr=- 12

We have found that r is either 6 or -12. Since a negative length radius does not make sense, we know that r = 6. We can now substitute 6 for r and 6 for h into the appropriate formula to calculate the volume of the cylinder.

V=π r^2 h

r= 6, h= 6

V=π ( 6)^2 ( 6)

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Simplify right-hand side

Calculate power

V=π( 36)( 6)

Multiply

V=216π

Use a calculator

V=678.584013...

Round to 1 decimal place(s)

V≈ 678.6

The approximate volume of the given cylinder is 678.6 in^3.

Subchapter links

Exercises p.834-838