Exercise 34 Page 738

We are told that the surface area of a sphere is 4π m^2 and want to find its volume.

We first need to find its radius. To do so, 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 4π for S.A. in the formula and solve for r.

S.A.=4π r^2

Substitute

S.A.= 4π

4π=4π r^2

▼

Solve for r

DivEqn

.LHS /4π.=.RHS /4π.

1=r^2

RearrangeEqn

Rearrange equation

r^2=1

RadicalEqn

sqrt(LHS)=sqrt(RHS)

r=1

The radius of a sphere with surface area 4π m^2 is 1m.

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

V=4/3π r^3

Substitute

r= 1

V=4/3π ( 1)^3

BaseOne

1^a=1

V=4/3π (1)

IdPropMult

Identity Property of Multiplication

V=4/3π

The volume of a sphere in terms of π with surface area 4π m^2 is 43π m^3.