Exercise 25 Page 737

We are told that the volume of a sphere is 140 cm^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 140 for V in the formula and solve for r.

V=4/3π r^3

Substitute

V= 140

140=4/3π r^3

▼

Solve for r

MultEqn

LHS * 3/4=RHS* 3/4

140(3/4)=π r^3

MoveLeftFacToNum

a*b/c= a* b/c

420/4=π r^3

CalcQuot

Calculate quotient

105=π r^3

DivEqn

.LHS /π.=.RHS /π.

105/π=r^3

RadicalEqn

sqrt(LHS)=sqrt(RHS)

sqrt(105/π)=r

RearrangeEqn

Rearrange equation

r=sqrt(105/π)

UseCalc

Use a calculator

r=3.221166...

RoundDec

Round to 2 decimal place(s)

r ≈ 3.22

The radius of a sphere with volume 140cm^3 is 3.22cm.

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 3.22, we can substitute its value for r into this formula.

S.A.=4π r^2

Substitute

r= 3.22

S.A.=4π ( 3.22)^2

UseCalc

Use a calculator

S.A.=130.293157...

RoundInt

Round to nearest integer

S.A.≈ 130

The surface area of a sphere correct to the nearest whole number with volume 140 cm^3 is 130cm^2.