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Mathematics · 2023 · 5 marks
CBSE 2023 · Region 6 · Set 1 · Q33
A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being 7 cm and the height of the cone is…
A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being $\displaystyle 7$ cm and the height of the cone is equal to its diameter. Find the volume of the solid.
Marking-scheme solution
Radius of cone = radius of hemisphere \(\displaystyle =7 \mathrm{~cm}\)
∴ Height of cone \(\displaystyle =14 \mathrm{~cm}\)
Volume of solid = Volume of hemisphere + volume of cone
\[\begin{aligned}
& =\frac{2}{3} \pi(7)^{3}+\frac{1}{3} \pi(7)^{2} 14 \\
& =\frac{1}{3} \times \frac{22}{7} \times 7 \times 7(14+14) \\
& =\frac{154}{3} \times 28=\frac{4312}{3} \mathrm{~cm}^{2} \text { or } 1437.33 \mathrm{~cm}^{2}
\end{aligned}
\]
\[\begin{aligned}
& =\frac{2}{3} \pi(7)^{3}+\frac{1}{3} \pi(7)^{2} 14 \\
& =\frac{1}{3} \times \frac{22}{7} \times 7 \times 7(14+14) \\
& =\frac{154}{3} \times 28=\frac{4312}{3} \mathrm{~cm}^{2} \text { or } 1437.33 \mathrm{~cm}^{2}
\end{aligned}
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.