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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Surface Areas and Volumes of Spheres

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Exercise 23 Page 852

The volume of a sphere is four-thirds the product of π and the cube of the radius.

179.8in^3

Practice makes perfect

We will find the volume of the given sphere.

The volume of a sphere is four-thirds the product of π and the cube of the radius. V=4/3π r^3 We are told that the circumference of the great circle is 22 inches. Let's use the formula for the circumference C of a circle to find the radius r.

C=2π r

C= 22

22=2π r

▼

Solve for r

.LHS /2π.=.RHS /2π.

22/2π=r

Rearrange equation

r=22/2π

Use a calculator

r≈ 3.5014

Let's now substitute 3.5014 for r in the formula for the volume and simplify the right-hand side.

V=4/3π r^3

r= 3.5

V=4/3π ( 3.5014)^3

▼

Evaluate right-hand side

Calculate power

V≈ 4/3π (42.926)

CommutativePropMult

Commutative Property of Multiplication

V≈ 4/3(42.926)π

MoveRightFacToNum

a/c* b = a* b/c

V≈ 171.705/3π

Use a calculator

V≈ 179.80...

Round to 1 decimal place(s)

V≈ 179.8

The volume of the sphere to the nearest tenth is 179.8in^3.

Subchapter links

Exercises p.852-855