A balloon has a circumference of 11 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter.

Answer 1

SA = 4πr^2
C = 2πr

we know 2πr = 11
2r = 11/π

so the surface area is

4πr^2 = (2πr)(2r) = 11(11/π) = 121/π = 39 cm^2

The word "approximate" here puzzles me.
It suggests that we do 121/π in our head, not too many students could do that.
Unless this is an old-fashioned textbook question and they want us to use 22/7 for π
then 121/(22/7)
= 121*7/22
= 11*7/2
= 77/2 = 38.5 or 39 as above

Answer 2

circumference (c) is ... 2 * π * r
... r = c / (2 π)

surface area (s) is ... 4 * π * r^2 = 4 * π * c^2 / (4 π^2) = c^2 / π