Question : A solid hemisphere of radius 8 cm is melted into N identical cone whose radius is 4 cm and height is 2 cm. Then, what is the value of N?
Option 1: 26
Option 2: 10
Option 3: 32
Option 4: 25
Correct Answer: 32
Solution :
Radius of hemisphere, $r$ = 8 cm
Volume of hemisphere = $\frac{4}{3} \pi r^3$
= $\frac{2}{3}× \frac{22}{7}× 8^3$
= $\frac{22528}{21}$
Radius of cone, $R$ = 4 cm
Height of cone, $H$ = 2 cm
Volume of cone = $\frac{1}{3} \pi R^2 H$
= $\frac{1}{3}× \frac{22}{7}×4^2×2$
= $\frac{704}{21}$
Let N be the number of identical cones.
N = $\frac{\text{volume of hemisphere}}{\text{volume of cone}}$
= $\frac{\frac{22528}{21}}{\frac{704}{21}}$
= 32
Hence, the correct answer is 32.
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