Question

66 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?

• A. 40 cm
• B. 45 cm
• C. 50 cm
• D. 55 cm

Answer 1

Answer:

A. 40 cm

Given:

• Radius of hemisphere (=10) cm

• The hemisphere is melted into 2 identical cones

• Radius of each cone (=5) cm

• Height of each cone (=h)

Since the material is conserved,

$\text{Volume of hemisphere} = 2 \times \text{Volume of one cone}$

Volume of hemisphere:

$\frac{2}{3}\pi (10)^3=\frac{2000}{3}\pi$

Volume of one cone:

$\frac{1}{3}\pi (5)^2h=\frac{25}{3}\pi h$

For two cones:

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

Equating the volumes:

$\frac{2000}{3}\pi=\frac{50}{3}\pi h$

Cancel $(\frac{\pi}{3}):$

$2000=50h$
$h=\frac{2000}{50}=40\text{ cm}$

Answer:

$\boxed{40\ \text{cm}}$