Question:
Two cylindrical vessels are filled with oil. Their radii are 15 cm, 12 cm and heights 20 cm, 16 cm respectively. Find the radius of a cylindrical vessel 21 cm in height, which will just contain the oil of the two given vessels.
Solution:
The volume of $1^{\text {st }}$ cylindrical vessel $=\pi \times(15)^{2} \times 20$
$=225 \times 20 \times \pi$
$=4500 \pi \mathrm{cm}^{2}$
The volume of $2^{\text {nd }}$ cylindrical vessel $=\pi \times(12)^{2} \times 16$
$=144 \times 16 \times \pi$
$=1304 \pi \mathrm{cm}^{3}$
Let r be the radius of vessel, which will just contain oil of the both vessels.
Therefore,
Volume of cylindrical vessel = sum of the volume of both vessels.
i.e.,
$\pi r^{2} h=4500 \pi+2304 \pi$
$r^{2}=\frac{6804}{21}$
$r^{2}=324$
$r=18 \mathrm{~cm}$