Exercise 37 Page 63

We are given the area of a circle and we are asked to find the circumference. We can do this in two steps.

Using the area, we can find the radius.
Using the radius, we can find the circumference.

Let's do this!

Finding the Radius

The formula A=π r^2 tells us about the relationship between the radius r and the area A of a circle. We can use the given area, 32π square units, to find the value of r.

A=π r^2

Substitute

A= 32π

32π=π r^2

▼

Solve for r

DivEqn

.LHS /π.=.RHS /π.

32=r^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(32)=r

RearrangeEqn

Rearrange equation

r=sqrt(32)

The radius of a circle with an area of 32π square units is sqrt(32) units.

Finding the Circumference

The formula C=2π r relates the radius r of a circle to the circumference C. We can use this formula, and the value of r, to find the circumference.

C=2π r

Substitute

r= sqrt(32)

C=2π( sqrt(32))

UseCalc

Use a calculator

C=35.543063...

RoundDec

Round to 1 decimal place(s)

C ≈ 35.5

The circumference of a circle with an area of 32π square units is 2 π sqrt(32) or about 35.5 units.

Hints

Check the answer

Practice exercises

Asses your skill

Finding the Radius

Finding the Circumference