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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 2 · Set 1 · Q37
The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are…
The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd. A circus tent is cylindrical upto a height of $\displaystyle 8$ m and conical above it. The diameter of the base is $\displaystyle 28$ m and total height of tent is $\displaystyle 18.5$ m.
Based on the above, answer the following questions :
(i)
Find slant height of the conical part.
(ii)
Determine the floor area of the tent.
(iii)
(a)
Find area of the cloth used for making tent.
OR
(b)
Find total volume of air inside an empty tent.
Marking-scheme solution
(i) Height of conical part \(\displaystyle =18.5-8=10.5 \mathrm{~m}\) Radius of conical part = $\displaystyle 14$ m
\[\text { Slant height }=\sqrt{(10.5)^{2}+(14)^{2}}=17.5 \mathrm{~m}
\]
(ii) Floor area \(\displaystyle =\frac{22}{7} \times 14 \times 14=616 \mathrm{~m}^{2}\)
(iii) (a) Area of cloth used
\[\begin{aligned}
& =2 \times \frac{22}{7} \times 14 \times 8+\frac{22}{7} \times 14 \times 17.5 \\
& =1474 \mathrm{~m}^{2}
\end{aligned}
\]
(iii) (b) Volume of air inside the tent
\[\begin{aligned}
& =\frac{22}{7} \times 14 \times 14 \times 8+\frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times 10.5 \\
& =7084 \mathrm{~m}^{3}
\end{aligned}
\]
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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.