A flask in the shape of a right… - CUET UG 2025 General Test PYQ

CUET UG 2025 — General Test Geometry

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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

Official previous-year question

Held on 30 May 2025 · Verified 13 Jul 2026.

Options

A
27 cm
B
42 cm
C
72 cm
D
24 cm

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Solution

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 a cylindrical flask whose radius is two-third of the radius of the base of the cone.

Let the radius of the conical flask be $r$ and the radius of the cylindrical flask be $R = \frac{2r}{3}$ .

Let the height of tea in the cylindrical flask be $H$ .

The volume of tea remains constant when poured from one flask to another.

Volume of cone $= \frac{1}{3}\pi r^2 h$

$= \frac{1}{3} \times \pi \times r^2 \times 36$

$= 12\pi r^2$

Volume of cylinder $= \pi R^2 H$

$= \pi \times \left(\frac{2r}{3}\right)^2 \times H$

$= \pi \times \frac{4r^2}{9} \times H$

$= \frac{4\pi r^2 H}{9}$

Since the volume of tea remains the same:

$12\pi r^2 = \frac{4\pi r^2 H}{9}$

$12 = \frac{4H}{9}$

$108 = 4H$

$H = 27$

Therefore, the height of tea in the cylindrical flask is 27 cm.

Your note

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