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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 22 Page 835

Use the formula for the volume of a cylinder.

About 2.52 feet

Practice makes perfect

We are asked to find the diameter of the following cylinder.

The purpose of the cylinder is to hold V_\text{sand}=10 cubic feet of sand. Let r be its radius. Let's use the formula for the volume of a cylinder and substitute the known values to find r.

V_\text{sand}=\pi r^2h

V_\text{sand}={\color{#0000FF}{10}}, h= 2

10=π r^2( 2)

▼

Solve for r

Multiply

10=2π r^2

.LHS /2π.=.RHS /2π.

10/2π=r^2

Rearrange equation

r^2=10/2π

π ≈ 3.1416

r^2≈10/2( 3.1416)

Multiply

r^2≈10/6.2832

Calculate quotient & Use a calculator

r^2≈ 1.591546

sqrt(LHS)=sqrt(RHS)

r≈sqrt(1.591546)

Calculate root & Use a calculator

r≈ 1.261565

Round to 2 decimal place(s)

r≈ 1.26

Therefore, the radius of the cylinder should be about 1.26 feet. This tells us that its diameter should be about 2* 1.26=2.52 feet.

Subchapter links

Exercises p.834-838