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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 51 Page 855

The surface area of a sphere is four times the product of π and the square of the radius.

H

Practice makes perfect

We want to find the surface area of a sphere.

Sphere with the radius marked

The surface area of a sphere is four times the product of π and the square of the radius.

S=4π r^2 We are told that the area of the great circle is 33 ft^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= 33

33=π r^2

▼

Solve for r

.LHS /π.=.RHS /π.

33/π=r^2

Rearrange equation

r^2=33/π

sqrt(LHS)=sqrt(RHS)

r=sqrt(33/π)

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 sqrt(33π) for r in the formula for the surface area and simplify the right-hand side.

S=4π r^2

r= sqrt(33/π)

S=4π ( sqrt(33/π))^2

▼

Simplify right-hand side

Calculate power

S=4π (33/π)

MoveLeftFacToNum

a*b/c= a* b/c

S=4π (33)/π

a/b=.a /π./.b /π.

S=4(33)

Multiply

S=132

The surface area of the given sphere is 132ft^2, which corresponds to answer H.

Subchapter links

Exercises p.852-855