Question : The volume of a right circular cone having a base diameter of 14 cm is 196$\pi$ cm3. Find the perpendicular height of this cone
Option 1: 10 cm
Option 2: 12 cm
Option 3: 14 cm
Option 4: 8 cm
Correct Answer: 12 cm
Solution :
Given: The volume of a right circular cone = $196\pi\ \text{cm}^3$
Diameter of base = 14 cm
Radius = 7 cm
Volume of the cone = $\frac{1}{3}\pi r^2 h$
⇒ $196\pi = \frac{1}{3}\pi r^2 h$
⇒ $196 = \frac{1}{3}\times7\times7\times h$
⇒ $h = 12\ \text{cm}$
Hence, the correct answer is 12 cm.
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