A conical vessel whose internal base radius is 18 cm and height 60 cm is full of a liquid. The entire liquid of the vessel is emptied into a cylindrical vessel with internal radius 15 cm. The height (in cm) to which the liquid rises in the cylindrical vessel is:
Answer & explanation
Correct answer: option 4
We know that,
Volume of cylinder = πr2h
Volume of cone = \(\frac{1}{3}\) πr2h
Volume of cone = \(\frac{1}{3}\) × π × 182 × 60 = π × 6480
According to the question,
The internal radius of the cylindrical vessel = 15 cm
Let the height = H
We know that,
Volume of cylinder = π × 152 × H
According to the question,
Volume of cone = Volume of cylinder
= π × 6480 = π × 152 × H
H = \(\frac{6480}{225}\) = 28.8 cm