Question

The $\frac{3}{4}$th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water.The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

Answer 1

Internal radius of conical vessel = 5 cm
Height = 24 cm

$\frac{3}{4}$th part of a conical vessel is full of water.

Volume of the water is conical vessel = $\frac{3}{4}$ × $\frac{1}{3}$ × $\pi$r²h

= $\frac{3}{4}$ × $\frac{1}{3}$ × $\pi$ × 5² × 24

= $\frac{1}{4}$ × $\pi$ × 5² × 24

= 150$\pi$

Suppose the height of level of water in the cylindrical vessel is h.

Radius of base of cylindrical vessel = 10 cm
So, volume of water in cylindrical vessel up to height h = $\pi$ × 10² ×h

Volume of the water is conical vessel = Volume of cylindrical vessel
⇒150$\pi$ = $\pi$ × 10² ×h

⇒ h = 1.5 cm