Question : If a right circular cone of height 24 cm has the circumference of its base 42$\pi$ cm, then the volume of the cone is: (Use $\pi=\frac{22}{7}$)
Option 1: 15211 cm3
Option 2: 11088 cm3
Option 3: 12034 cm3
Option 4: 21011 cm3
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Correct Answer: 11088 cm 3
Solution : Given, the height of the cone, $h$ = 24 cm Let the radius of the cone be $r$ cm. Circumference of the base of the cone = 42$\pi$ cm ⇒ $2\pi r = 42\pi$ ⇒ $r=21\ cm$ Volume of cone = $\frac{1}{3}\pi r^2h$ = $\frac{1}{3}\times \frac{22}{7} \times (21)^2\times 24$ = $11088$ cm 3 Hence, the correct answer is 11088 cm 3 .
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