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 completly .state how will you decide the radius and perpendicular height of cone

Answer 1

Volume of bowl = 2 volume of cone

Hemisphere = cone

2/3 × pie r^3 = 2 (1/3 pie R^2 h)

2 × pie r^3 = 6 ( 1/3 pie R^2 h)

2 × pie r^3 = 2 ( pie R^2 h)

Pie r^3 = 2 ( pie R^2 h) ÷ 2

Pie r^3 = pie R^2 h

r^3 = (pie R^2 h) ÷ pie

r^3 = R^2 h

r^3 ÷ R^2 = h

h = r^3 / R^2

Hence we can put the values of radius of cone and hemispherical bowl and find height of cone.