Exercise 29 Page 754

We are told that the surface area of a sphere is 452.39 cm^2 and want to find its volume.

We first need to find its radius. To find the radius, we will use the formula for 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.A.=4π r^2Let's substitute 452.39 for S.A in the formula and solve for r.

S.A.=4π r^2

Substitute

S.A.= 452.39

452.39=4π r^2

▼

Solve for r

DivEqn

.LHS /4π.=.RHS /4π.

452.39/4π = r^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(452.39/4π) = r

RearrangeEqn

Rearrange equation

r=sqrt(452.39/4π)

UseCalc

Use a calculator

r = 6.000004...

RoundInt

Round to nearest integer

r ≈ 6

The radius of a sphere with surface area 452.39 cm^2 is approximately 6cm.

Now, let's find the volume of the sphere. The volume of a sphere is four thirds the product of π and the cube of the radius. V=4/3π r^3 Since we already know that the radius is 6, we can substitute its value for r into this formula.

V=4/3π r^3

Substitute

r= 6

V=4/3π ( 6)^3

UseCalc

Use a calculator

V = 904.778684...

RoundDec

Round to 2 decimal place(s)

V≈ 904.78

The volume of a sphere to the nearest hundredth, with surface area 452.39 cm^2, is 904.78cm^3.