Question

There is a hemispherical bowl. A cone is to
be made such that, if it is filled with water
twice and the water poured in the bowl, it
will be filled just completely. State how will
you decide the radius and perpendicular
height of the cone.

Answer 1

Answer :

• So, radius of base of the cone is R and its height is R, which is equal to radius of the bowl, then a cone satisfying the given condition can be made.

Given :

• A cone is to be made such that, if it is filled with water twice and the water poured in the bowl, it will be filled just completely.

To find :

• State how will you decide the radius and perpendicular height of the cone.

Step-by-step explanation :

Volume of hemisphere = 2/3 πR3

Volume of hemisphere = 2/3 πR3 Volume of cone = 1/3 πr2 × h

By the given condition ;

2 × volume of cone = volume of hemisphere

∴ 2 × 1 / 3 πr2 h = 2 3 πR3

∴ r2 h = R3

∴ if, r = h = R

Then both sides will be equal.

∴ if radius of base of the cone is R and its height is R, which is equal to radius of the bowl, then a cone satisfying the given condition can be made.