The (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.

Radius of cone = r = 5 cm

Height of cone = h = 24 cm

Volume of cone = (1/3)πr²h

= (1/3) × π × 25 × 24

= 200π cm³

3/4th volume of cone = 3/4 × 200π = 150π cm³

∴ Volume of water in cone = 150 cm³

Radius of cylindrical vessel = R =10 cm

Let height of the cylindrical vessel = H (say)

Volume of water = Volume of cylindrical vessel = πr²h

∴ πR²H = 150π

⇒ R²H = 150

⇒ (10)²H = 150

⇒ 100H = 150

⇒ H = 150/100 = 1.5 cm

∴ Height of the cylindrical vessel = 1.5 cm