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

27 cm

The correct answer is Option (1) → 27 cm

Given:

• A cone of height $h_c = 36$ cm
• Radius of cone $r_c = r$ (let's call it r)
• The cone is filled with tea.
• The tea is poured into a cylinder with radius $r_{\text{cyl}} = \frac{2}{3} r$r
• Find height $h_{\text{cyl}}$​ of tea in cylinder.

Step 1: Volume of the cone

$V_{\text{cone}} = \frac{1}{3}\pi r^2 h_c = \frac{1}{3}\pi r^2 (36) = 12 \pi r^2$

Step 2: Volume of the cylinder

$V_{\text{cyl}} = \pi r_{\text{cyl}}^2 h_{\text{cyl}} = \pi \left(\frac{2}{3}r\right)^2 h_{\text{cyl}} = \pi \frac{4}{9} r^2 h_{\text{cyl}}$

Step 3: Equate volumes

$12 \pi r^2 = \pi \frac{4}{9} r^2 h_{\text{cyl}}$

Divide both sides by $\pi r^2$:

$12 = \frac{4}{9} h_{\text{cyl}}$

$h_{\text{cyl}} = 12 \times \frac{9}{4} = 27 \text{ cm}$

Answer: 27 cm