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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 8 Page 852

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

1708.6in^3

Practice makes perfect

Consider 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 given the area of the great circle, 55π in^2.

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

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

A=π r^2

A= 55π

55π=π r^2

▼

Solve for r

.LHS /π.=.RHS /π.

55=r^2

sqrt(LHS)=sqrt(RHS)

sqrt(55)=r

Rearrange equation

r=sqrt(55)

Let's now substitute sqrt(55) for r in the formula for the volume and simplify the right-hand side.

V=4/3π r^3

r= sqrt(55)

V=4/3π ( sqrt(55))^3

Use a calculator

V=1708.56...

Round to 1 decimal place(s)

V≈ 1708.6

The volume of the sphere to the nearest tenth is 1708.6in^3.

Subchapter links

Exercises p.852-855