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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 3 · Set 1 · Q35
(a) A solid iron pole consists of a solid cylinder of height 200 cm and base diameter 28 cm, which is surmounted by another cylinder of height 50 cm…
A solid iron pole consists of a solid cylinder of height $\displaystyle 200$ cm and base diameter $\displaystyle 28$ cm, which is surmounted by another cylinder of height $\displaystyle 50$ cm and radius $\displaystyle 7$ cm. Find the mass of the pole, given that $\displaystyle 1 \mathrm{~cm}^{3}$ of iron has approximately $\displaystyle 8$ g mass.
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is $\displaystyle 14$ mm and the diameter of the capsule is $\displaystyle 4$ mm, find its surface area. Also, find its volume.
Marking-scheme solution
Radius of lower cylinder \(\displaystyle =14 \mathrm{~cm}\)
\[\begin{aligned}
& \text { Volume of pole }=\frac{22}{7} \times 14 \times 14 \times 200+\frac{22}{7} \times 7 \times 7 \times 50 \\
& \quad=130900 \mathrm{~cm}^{3}
\end{aligned}
\]
Mass of the pole \(\displaystyle =8 \times 130900\)
\[=1047200 \mathrm{gm} \text { or } 1047.2 \mathrm{~kg}
\]
Radius of hemisphere= radius of cylinder = $\displaystyle 2$ mm
Length of cylindrical part = \(\displaystyle 14-4=10 \mathrm{~mm}\).
Surface area of the capsule = CSA of cylinder + $\displaystyle 2$(CSA of hemisphere)
\[\begin{aligned}
& =2 \times \frac{22}{7} \times 2 \times 10+2 \times 2 \times \frac{22}{7} \times 2 \times 2 \\
& =176 \mathrm{~mm}^{2}
\end{aligned}
\]
Volume of the capsule = volume of cylinder + $\displaystyle 2$(volume of hemisphere)
\[\begin{aligned}
& =\frac{22}{7} \times 2 \times 2 \times 10+2 \times \frac{2}{3} \times \frac{22}{7} \times 2 \times 2 \times 2 \\
& =\frac{3344}{21} \mathrm{~mm}^{3} \text { or } 159.24 \mathrm{~mm}^{3}
\end{aligned}
\]
All Surface Areas and Volumes questions2024 question paperNCERT solutions: Surface Areas and VolumesPractice Surface Areas and Volumes →
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CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.