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.

Answer 1

The volume of 1^st cylindrical vessel `= pi xx (15)^2 xx 20`

                                                           `= 225 xx 20 xx pi`

                                                           `= 4500pi cm^2`

The volume of 2^nd cylindrical vessel `= pi xx (12)^2 xx 16`

                                                           `= 144 xx 16 xx pi`

                                                           `= 1304pi 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.,

`pir^2 h = 4500pi + 2304 pi`

`pir^2 xx 21 = 6804 pi`

`r^2 = (6804)/21`

`r^2 = 324`

`r = 18cm`