Question : If the height of a cone is 7 cm and the diameter of the circular base is 12 cm, then its volume is (nearest to integer):
Option 1: $254\; \text{cm}^3$
Option 2: $284\; \text{cm}^3$
Option 3: $264\; \text{cm}^3$
Option 4: $274\; \text{cm}^3$
Correct Answer: $264\; \text{cm}^3$
Solution : The volume V of a cone can be calculated using the formula: $V = \frac{1}{3} \pi r^2 h$ where r is the radius of the base and h is the height of the cone. Given that the diameter of the base is 12 cm, the radius r is 6 cm. The height h is given as 7 cm. Substituting these values into the formula gives: $V = \frac{1}{3} × \frac{22}{7} × 6^2 × 7$ $V= 264 \;\text{cm}^3$ Hence, the correct answer is $264\; \text{cm}^3$.
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