The radius of a conical vessel is 10 cm and its height is 18 cm. It is

1.	The radius of a conical vessel is 10 cm and its height is 18 cm. It is completely filled with water. The water is pored into another cylindrical vessel with radius 5 cm. Find the height of water in this vessel.
Answer» Given, Radius of conical vessel (R) = 10 cm and its height = 18 cm Volume of conical vessel = \(\frac { 1 }{ 3 }\)r²h = \(\frac { 1 }{ 3 }\) × π × (10)² × 18 = \(\frac { 1 }{ 3 }\) × π × 100 × 18 π × 100 × 6 = 600 π cm³. Let the height of water in cylindrical vessel be H and its radius = 5 cm. Now, according to question. Volume of cylindrical vessel = Volume of water in the conical vessel. πR²H = 600 π π(5)²H = 600 π H = \(\frac { 600\pi }{ 25\pi } \) = 24 cm Hence, height of water in cylindrical vessel = 24 cm

The radius of a conical vessel is 10 cm and its height is 18 cm. It is completely filled with water. The water is pored into another cylindrical vessel with radius 5 cm. Find the height of water in this vessel.

Answer»

Given,

Radius of conical vessel (R) = 10 cm

and its height = 18 cm

Volume of conical vessel = \(\frac { 1 }{ 3 }\)r²h

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

= \(\frac { 1 }{ 3 }\) × π × 100 × 18

π × 100 × 6

= 600 π cm³.

Let the height of water in cylindrical vessel be H and its radius = 5 cm.

Now, according to question.

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

πR²H = 600 π

π(5)²H = 600 π

H = \(\frac { 600\pi }{ 25\pi } \) = 24 cm

Hence, height of water in cylindrical vessel = 24 cm