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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 2 · Set 1 · Q14
Case Study - $\displaystyle 2$ A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around $\displaystyle 250$ years back, in open fields, now generally performed in tents. One such 'Circus Tent' is shown below.
The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are $\displaystyle 9$ m and $\displaystyle 30$ m respectively and height of conical part is $\displaystyle 8$ m with same diameter as that of the cylindrical part, then find(1)the area of the canvas used in making the tent;(2)the cost of the canvas bought for the tent at the rate ₹ $\displaystyle 200$ per sq m, if $\displaystyle 30$ sq m canvas was wasted during stitching.
Case Study - $\displaystyle 2$ A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around $\displaystyle 250$ years back, in open fields, now generally performed in tents. One such 'Circus Tent' is shown below.
The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are $\displaystyle 9$ m and $\displaystyle 30$ m respectively and height of conical part is $\displaystyle 8$ m with same diameter as that of the cylindrical part, then find
(1)
the area of the canvas used in making the tent;
(2)
the cost of the canvas bought for the tent at the rate ₹ $\displaystyle 200$ per sq m, if $\displaystyle 30$ sq m canvas was wasted during stitching.
Marking-scheme solution
1. 1.
\[l=\sqrt{8^{2}+15^{2}}=17 \mathrm{~m}
\]
\[\text { Area of canvas used }=\pi r l+2 \pi r h
\]
\[=\pi r(l+2 h)
\]
\[=\frac{22}{7} \times 15(17+18)
\]
\[=1650 \mathrm{~m}^{2}
\]
\[\text { Canvas used }=1650+30=1680 \mathrm{~m}^{2}
\]
\[\begin{aligned}
\therefore \text { cost of canvas used } & =200 \times 1680 \\
& =₹ 3,36,000
\end{aligned}
\]More from Surface Areas and Volumes
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CBSE Class 10 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.