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McGraw Hill Integrated II, 2012 View details

6. Surface Areas and Volumes of Spheres

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Exercise 22 Page 852

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

1436.8m^3

Practice makes perfect

We want to 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 area of the great circle is 49π m^2.

Notice that the sphere and the great circle have the same radius. Let's use the formula for the area A of a circle to find the radius r.

A=π r^2

Substitute

A= 49π

49π=π r^2

▼

Solve for r

DivEqn

.LHS /π.=.RHS /π.

49=r^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

7=r

RearrangeEqn

Rearrange equation

r=7

Since r is a radius it must be nonnegative, which is why we only kept the principal root when solving the equation. Let's now substitute 7 for r in the formula for the volume and simplify the right-hand side.

V=4/3π r^3

Substitute

r= 7

V=4/3π ( 7)^3

▼

Evaluate right-hand side

CalcPow

Calculate power

V=4/3π (343)

CommutativePropMult

Commutative Property of Multiplication

V=4/3(343)π