A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed? - Quantitative Aptitude MCQ SSC CGL 2026 | ExamTest.live

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A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

Solution & Step-by-step Explanation

Given: Diameter = 10 cm ⟹ Radius (r) = 5 cm Height of cone (h) = 12 cm The solid consists of a cone and a hemisphere. Volume of solid = Volume of cone + Volume of hemisphere Volume = \frac{1}{3} π r^{2} h + \frac{2}{3} π r^{3} = \frac{1}{3} π r^{2} (h + 2 r) Substituting the values: Volume = \frac{1}{3} \times \frac{22}{7} \times 5^{2} \times (12 + 2 (5)) Volume = \frac{1}{3} \times \frac{22}{7} \times 25 \times 22 Volume = \frac{12100}{21} \approx 576.19 cm^{3}

Try it yourself before checking the explanation above.

A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

384.13 cm^{3}

576.19 cm^{3}

192.06 cm^{3}

288.1 cm^{3}

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