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 [tex]S.A=4\pi r^{2}[/tex]
Circumference of sphere is [tex]C=2\pi r[/tex]
We have to find the radius using circumference.
Given C=28
[tex]r=\frac{C}{2\pi}[/tex]
[tex]r=\frac{28}{2\pi}[/tex]
[tex]r=\frac{14}{\pi}[/tex]
Substitute the value of r in the formula of surface area,
[tex]S.A=4\pi r^{2}[/tex]
[tex]S.A=4\pi (\frac{14}{\pi})^{2}[/tex]
[tex]S.A=4\pi \times \frac{196}{\pi^2}[/tex]
[tex]S.A=4\times \frac{196}{\pi}[/tex]
Put [tex]\pi=3.14[/tex]
[tex]S.A=4\times \frac{196}{3.14}[/tex]
[tex]S.A=4\times 62.42[/tex]
[tex]S.A=249.68in^2[/tex]
Nearest square inch = 250 square inch.
Therefore, The surface area of the balloon 250 sq. in.
