Question

A spherical shaped water ballon has a surface area of 113. 04 square inches how may cubic inches of water will the ballon hold? Express your answer in terms of pie

Answer 1

The balloon can hold
`(200.31)/(\pi ) in^3` of water.

Explanation:

Formula for surface area: A = 4πr²

Since we are given the surface area, we can solve for r using the formula above.

Solve for r (radius)

A = 4πr²

113.04 in² = 4πr²

113.04/4π = r²

28.26/π = r²

r = √(28.26/π) inches

Since we're asked of how much water the balloon can hold then we have to find the volume.

Formula: V = 4/3πr³

Substitute the value of r and then solve for the volume in terms of pi

V = 4/3πr³

V = 4/3π(√(28.26/π))³

`V = (4)/(3)\pi(\sqrt{ (28.26)/(\pi) })^3\\V = (4)/(3)\pi (\sqrt{ (28.26)/(\pi) })^2(\sqrt{ (28.26)/(\pi) })\\V = (4)/(3)\pi ((28.26)/(\pi ) )(\sqrt{(28.26)/(\pi ) }) \\V = (4(28.26))/(3) (\sqrt{(28.26)/(\pi ) })\\V = 37.68(\sqrt{(28.26)/(\pi ) })\\V = (200.31)/(\pi )`