Exercise 23 Page 737

We are told that the volume of a sphere is 900 in.^3 and want to find its surface area.

We first need to find its radius. To find the radius, we will use the formula for the volume of a sphere. The volume of a sphere is four thirds the product of π and the cube of the radius. V=4/3π r^3Let's substitute 900 for V in the formula and solve for r.

V=4/3π r^3

Substitute

V= 900

900=4/3π r^3

▼

Solve for r

MultEqn

LHS * 3/4=RHS* 3/4

900(3/4)=π r^3

MoveLeftFacToNum

a*b/c= a* b/c

2700/4=π r^3

CalcQuot

Calculate quotient

675=π r^3

DivEqn

.LHS /π.=.RHS /π.

675/π=r^3

RadicalEqn

sqrt(LHS)=sqrt(RHS)

sqrt(675/π)=r

RearrangeEqn

Rearrange equation

r=sqrt(675/π)

UseCalc

Use a calculator

r=5.989418...

RoundDec

Round to 2 decimal place(s)

r ≈ 5.99

The radius of a sphere with volume 900in.^3 is 5.99inches.

Now, let's find the surface area of the sphere. The surface area of a sphere is four times the product of π and the square of the radius. S.A.=4π r^2 Since we already know that the radius is 5.99, we can substitute its value for r into this formula.

S.A.=4π r^2

Substitute

r= 5.99

S.A.=4π ( 5.99)^2

UseCalc

Use a calculator

S.A.=450.882634...

RoundInt

Round to nearest integer

S.A.≈ 451

The surface area of a sphere correct to the nearest whole number with volume 900 in.^3 is 451in.^2.