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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 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.

Sphere with the radius marked

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.

Sphere with the radius and the area of the great circle marked

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

A= 49π

49π=π r^2

▼

Solve for r

.LHS /π.=.RHS /π.

49=r^2

sqrt(LHS)=sqrt(RHS)

7=r

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

r= 7

V=4/3π ( 7)^3

▼

Evaluate right-hand side

Calculate power

V=4/3π (343)

CommutativePropMult

Commutative Property of Multiplication

V=4/3(343)π

MoveRightFacToNum

a/c* b = a* b/c

V=1372/3π

Use a calculator

V=1436.75...

Round to 1 decimal place(s)

V≈ 1436.8

The volume of the sphere to the nearest tenth is 1436.8m^3.

Subchapter links

Exercises p.852-855