The section of a solid right circular cone by a plane containing vertex and perpendicular to base is an equilateral triangle of side 14 cm. What is the volume of the cone? (\pi=\frac{22}{7})
- A. 1078\sqrt{3} cubic cm
- B. \frac{1078}{\sqrt{3}} cubic cm ✓
- C. 539\sqrt{3} cubic cm
- D. \frac{539}{\sqrt{3}} cubic cm
Correct Answer: B. \frac{1078}{\sqrt{3}} cubic cm
Explanation
The section is a triangle with base equal to the diameter 2r and sides equal to slant height l. Being equilateral, 2r = 14 \implies r = 7, and l = 14. Height h = \sqrt{14^2-7^2} = 7\sqrt{3}. Volume = \frac{1}{3}\pi r^2 h = \frac{1}{3}(\frac{22}{7})(49)(7\sqrt{3}) = \frac{1078}{\sqrt{3}} cm^3.
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