Question

A balloon is in the form of right circular cylinder of radius 1.5 m and length 4 m and is surmounted by hemispherical ends. If the radius is increased by 0.01 m and the length by 0.05 m, the approxi- mate percentage change in the volume of the balloon is

Answer 1

Volume of the cylinder:

Volume = πr²h

Volume = π(1.5)²(4) = 9π m³

Volume of the hemisphere:

Volume = 1/2 (4/3πr³)

Volume = 1/2 (4/3π(1.5)³)

Volume = 1/2 (4/3π(1.5)³) = 2.25π m³

Find the total volume:

Total volume = 9π + 2.25π = 11.25π m³

Volume of the cylinder after the increase:

Volume = πr²h

Volume = π(1.5+ 0.01)²(4+ 0.05) = 9.234π m³

Volume of the hemisphere after the increase:

Volume = 1/2 (4/3πr³)

Volume = 1/2 (4/3π(1.5 + 0.01)³)

Volume = 2.295π m³

Find the total volume:

Total volume = 9.234π + 2.295π = 11.295π m³

Find the percentage change:

Change in percentage = (11.295π - 11.25) / 11.25 x 100 = 2.48%

Answer: The approximate change in volume is 2.48%