A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into another right circular cylindrical flask whose radius is two-third of the radius of base of the circular cone. Then, the height of the tea in the cylindrical flask is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 27 cm
When a liquid is poured from one vessel into another, its volume stays the same. So the volume of the cone is set equal to the volume of tea in the cylinder. Let the radius of the cone be \(r\); the radius of the cylinder is then \(\frac{2}{3}r\).
The two volumes:
Volume of the cone \(\displaystyle =\frac{1}{3}\pi r^2\times36=12\pi r^2\)
Volume of tea in the cylinder, height \(h\): \(\displaystyle \pi\left(\frac{2r}{3}\right)^2 h=\frac{4}{9}\pi r^2 h\)
Finding \(h\) (equating the two):
\(\displaystyle \frac{4}{9}\pi r^2 h=12\pi r^2\)
\(\displaystyle h=\frac{12\times9}{4}=27\) cm
