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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 5 · Set 1 · Q35
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 5…
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is $\displaystyle 5 \cdot 8$ cm and its base is of radius $\displaystyle 2 \cdot 1$ cm, find the total surface area of the article.

Marking-scheme solution
\[\begin{aligned}
\text { CSA of cylinder } & =2 \times \frac{22}{7} \times 2.1 \times 5.8 \\
& =76.56 \mathrm{~cm}^{2} \\
\text { CSA of two hemisphere } & =4 \times \frac{22}{7} \times 2.1 \times 2.1 \\
& =55.44 \mathrm{~cm}^{2}
\end{aligned}
\]
Total Surface Area of article \(\displaystyle =76.56+55.44=132 \mathrm{~cm}^{2}\)
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