Question : The volume of a cone is 73920 cm3. If the height of the cone is 160 cm, find the diameter of its base.
Option 1: 21 cm
Option 2: 40 cm
Option 3: 22 cm
Option 4: 42 cm
Correct Answer: 42 cm
Solution :
Given: The volume of the cone is 73920 cm
3
Height = 160 cm
We know that the volume of a cone with radius $r$ and height $h =\frac{1}{3}\pi r^2 h$
Now, $\frac{1}{3}\pi r^2 h = 73920$
⇒ $\frac{1}{3}×\frac{22}{7}×r^2×160 = 73920$
⇒ $r^2 = \frac{73920×3×7}{160×22}$
⇒ $r^2 = 441$
⇒ $r = 21$
Diameter = 2$r$ = 2 × 21 = 42 cm
Hence, the correct answer is 42 cm.
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