Exercise 51 Page 855

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

Practice makes perfect

We want to find the surface area of a sphere.

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.

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= 33

33=π r^2

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Solve for r

DivEqn

.LHS /π.=.RHS /π.

33/π=r^2

RearrangeEqn

Rearrange equation

r^2=33/π

SqrtEqn

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

Substitute

r= sqrt(33/π)

S=4π ( sqrt(33/π))^2

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Simplify right-hand side

CalcPow

Calculate power

S=4π (33/π)

MoveLeftFacToNum

a*b/c= a* b/c

S=4π (33)/π