Question

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

• A. $2.38\%$
• B. $2.48\%$
• C. $2.038\%$
• D. $2.58\%$

Answer 1

The correct option is B $2.48\%$

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

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

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

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