Question

A balloon has a circumference of 28 in. Use the circumference to approximate the surface area of the balloon to the nearest square inch.

Answer 1

C=2πr

r=C/(2π), now the surface area is:

A=4πr^2, using r found above we have:

A=4πC^2/(4π^2)

A=C^2/π, we are given that C=28 so:

A=28^2/π in^2

A=784/π in^2

A≈250 in^2 (to nearest square inch)

Answer 2

The surface area of the balloon 250 sq. in.

Explanation:

Given : A balloon has a circumference of 28 in.

To find : The surface area of the balloon to the nearest square inch using the circumference.

Solution :

The surface area of sphere is
`S.A=4\pi r^(2)`

Circumference of sphere is
`C=2\pi r`

We have to find the radius using circumference.

Given C=28

`r=(C)/(2\pi)`

`r=(28)/(2\pi)`

`r=(14)/(\pi)`

Substitute the value of r in the formula of surface area,

`S.A=4\pi r^(2)`

`S.A=4\pi ((14)/(\pi))^(2)`

`S.A=4\pi * (196)/(\pi^2)`

`S.A=4* (196)/(\pi)`

Put
`\pi=3.14`

`S.A=4* (196)/(3.14)`

`S.A=4* 62.42`

`S.A=249.68in^2`

Nearest square inch = 250 square inch.

Therefore, The surface area of the balloon 250 sq. in.