A solid hemisphere of radius 10 cm is melted into two cones of equal height. If each cone’s radius is 5 cm, what is the height of each cone?

Correct option is A

​Given :

Radius of solid hemisphere R = 10 cm
The hemisphere is melted into two identical cones
Radius of each cone r = 5 cm

Formula Used :

Volume of hemisphere
​$$V_{\text{hemisphere}} = \frac{2}{3}\pi R^3$$​​

Volume of cone
​$$V_{\text{cone}} = \frac{1}{3}\pi r^2 h$$​​

Solution :

​Height of each cone = h

Volume of hemisphere:
V =$$\frac{2}{3}\pi (10)^3$$ ​

​$$= \frac{2}{3}\pi \times 1$$​000 

​$$= \frac{2000}{3}\pi$$​​

Volume of two cones:
2$$\times \frac{1}{3}\pi (5)^2 h$$ ​

​$$= 2 \times \frac{25}{3}\pi h$$​​
​$$= \frac{50}{3}\pi h$$​​

Since volume is conserved:
​$$\frac{2000}{3}\pi = \frac{50}{3}\pi h$$​​

2000 = 50h
h = 40

Height of each cone = 40 cm