Question

A balloon is in the form of right circular cylinder of radius $1.5m$ length $4m$ and is surmounted by hemi spherical ends. If the radius is increased by $0.01m$ & the length by $0.05m$ , the percentage change in the volume of balloon is $abcd\%$, then the value of abcd must be ?

• A. $2.48$
• B. $1734$
• C. $9374$
• D. N.O.T

Answer 1

The correct option is A $2.48$

Volume of the cylinder:

Volume $=\pi r²h$

Volume $=\pi \left(1.5\right)²\left(4\right)=9\pi m³$

Volume of the hemisphere:

Volume $=\frac{1}{2}\left(\frac{4}{3}\pi r³\right)$

Volume $=\frac{1}{2}\left(\frac{4}{3}\pi \right(1.5\left)³\right)=2.25\pi m^3$

Find the total volume:

Total volume $=9\pi +2.25\pi =11.25\pi m³$

Volume of the cylinder after the increase:

Volume $=\pi r²h$

Volume $=\pi (1.5+0.01)²(4+0.05)=9.234\pi m³$

Volume of the hemisphere after the increase:

Volume $=\frac{1}{2}\left(\frac{4}{3}\pi r³\right)$

Volume $=\frac{1}{2}\left(\frac{4}{3}\pi \right(1.5+0.01\left)³\right)=2.295\pi m³$

Find the total volume:

Total volume $=9.234\pi +2.295\pi =11.295\pi m³$

Find the percentage change:

Change in percentage $=\frac{(11.295\pi -11.25)}{11.25\ast 100}=2.48$