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.

Answer 1

Let, the perpendicular height of cone be 'h'.
Let, the radius of base of cone be 'r'

Volume of cone =
$\frac{1}{3} \pi {r}^{2} h$
By given condition-
Volume of sphere = 2 × Volume of cone
$\frac{2}{3} \pi {r}^{3} = 2 \times \frac{1}{3} \pi {r}^{2} h$
After calculating-
$r = h$
Ans. The radius and height of cone must be equal to fill the spherical bowl in 2 attempts.

Answer 2

Answer:

Step-by-step explanation:

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 valuse of radiusof cone and hemispherical bowl and find height of cone