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

Answer:

The surface area of the balloon 250 sq. in.

Step-by-step 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

$r=\frac{C}{2\pi}$

$r=\frac{28}{2\pi}$

$r=\frac{14}{\pi}$

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

$S.A=4\pi r^{2}$

$S.A=4\pi (\frac{14}{\pi})^{2}$

$S.A=4\pi \times \frac{196}{\pi^2}$

$S.A=4\times \frac{196}{\pi}$

Put $\pi=3.14$

$S.A=4\times \frac{196}{3.14}$

$S.A=4\times 62.42$

$S.A=249.68in^2$

Nearest square inch = 250 square inch.

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