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
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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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