A conical vessel with base radius 10 cm. contains some water in it. Th

1.	A conical vessel with base radius 10 cm. contains some water in it. The water level in the vessel is 18 cm high. It is pored into another cylindrical vessel with radius 5 cm. Find the water level in the cylindrical vessel.
Answer» Base radius of conical vessel (R) = 10 cm And the height (H) = 18 cm Volume of conical vessel = \(\frac { 1 }{ 3 }\)πR²H = \(\frac { 1 }{ 3 }\) × π × (10)² × 18 = π ×100 × 6 = 600 π cm³ Let the water lavel in the cylindrical vessel be h. Radius (r) = 5 cm. Now according to the problem Volume of water in the cylindrical vessel = Volume of water in conical vessel πr²h = 600 π or r²h = 600 ⇒ (5)²h = 600 ⇒ 25 h = 600 h = \(\frac { 600 }{ 25 }\) = 24 cm Hence the water level in the cylindrical vessel = 24 cm.

A conical vessel with base radius 10 cm. contains some water in it. The water level in the vessel is 18 cm high. It is pored into another cylindrical vessel with radius 5 cm. Find the water level in the cylindrical vessel.

Answer»

Base radius of conical vessel (R) = 10 cm

And the height (H) = 18 cm

Volume of conical vessel = \(\frac { 1 }{ 3 }\)πR²H

= \(\frac { 1 }{ 3 }\) × π × (10)² × 18

= π ×100 × 6

= 600 π cm³

Let the water lavel in the cylindrical vessel be h.

Radius (r) = 5 cm.

Now according to the problem

Volume of water in the cylindrical vessel = Volume of water in conical vessel

πr²h = 600 π

or r²h = 600

⇒ (5)²h = 600

⇒ 25 h = 600

h = \(\frac { 600 }{ 25 }\)

= 24 cm

Hence the water level in the cylindrical vessel = 24 cm.