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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