A cone of height 16 cm and diameter 14 cm is mounted on a hemisphere of same diameter. What is the volume of the solid thus formed? (take \pi=\frac{22}{7})

  1. A. 1540\text{ cm}^{3} ✓
  2. B. 1078\text{ cm}^{3}
  3. C. 1048\text{ cm}^{3}
  4. D. 770\text{ cm}^{3}

Correct Answer: A. 1540\text{ cm}^{3}

Explanation

Radius r = \frac{14}{2} = 7\text{ cm}. Volume of cone = \frac{1}{3}\pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times 49 \times 16 = \frac{2464}{3}\text{ cm}^3. Volume of hemisphere = \frac{2}{3}\pi r^3 = \frac{2}{3} \times \frac{22}{7} \times 343 = \frac{2156}{3}\text{ cm}^3. Total Volume = \frac{2464+2156}{3} = \frac{4620}{3} = 1540\text{ cm}^3.

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