Question

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

Answer 1

||✪✪ QUESTION ✪✪||

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

|| ★★ FORMULA USED ★★ ||

• Volume of Hemisphere = (2/3) * π * r³
• Volume of cone = (1/3) * π * R² * H

|| ✰✰ ANSWER ✰✰ ||

Given That,

2 * Volume of cone = volume of Hemi-Sphere .

Putting both formula here ,

→ 2 * (1/3) * π * R² * H = (2/3) * π * r³

→ (2/3) * π * R² * H = (2/3) * π * r³

(2/3) and π will be cancel Now,

→ R²H = r³

Now, we can see that , if R = H = r , then both sides will be equal.

Hence, 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.