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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 4 · Set 1 · Q12
From the top of an $\displaystyle 8$ m high building, the angle of elevation of the top of a cable tower is $\displaystyle 60^{\circ}$ and the angle of depression of its foot is $\displaystyle 45^{\circ}$. Determine the height of the tower. (Take $\displaystyle \sqrt{3}=1.732$ ). Case Study - $\displaystyle 1$
Marking-scheme solution
\(\displaystyle \therefore l=55, f=40, c f=58, h=10\)
\[\begin{aligned}
& \begin{aligned}
\text { Median } & =l+\frac{\dfrac{N}{2}-c f}{f} \times h \\
& =55+\frac{70-58}{40} \times 10=55+3=58
\end{aligned} \\
& \therefore \text { Median } \\
& =58
\end{aligned}
\]
\[=\pi \times(1.5)^{2} \times 4 \mathrm{~cm}^{3}
\]
Radius of hemisphere \(\displaystyle R=9 \mathrm{~cm}\)
Volume of hemisphere \(\displaystyle =\frac{2}{3} \pi R^{3}\)
\[=\frac{2}{3} \times \pi \times(9)^{3} \mathrm{~cm}^{3}
\]
Let the number of cylindrical jars be \(\displaystyle n\)
\[\begin{aligned}
& \therefore n \times \pi \times(1.5)^{2} \times 4=\frac{2}{3} \times \pi \times(9)^{3} \\
& \Rightarrow \mathrm{n}=\frac{9 \times 9 \times 9 \times 2}{4 \times 1.5 \times 1.5 \times 3}=54
\end{aligned}
\]
∴ Number of cylindrical jars required = $\displaystyle 54$
(b)
For conical funnel, \(\displaystyle r=\frac{3}{2} c m, h=4 c m\)
\[\begin{aligned}
\therefore \text { Volume of conical funnel } & =\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times \frac{22}{7} \times \frac{3}{2} \times \frac{3}{2} \times 4 \\
& =\frac{66}{7} c m^{3} \text { of water will flow out. }
\end{aligned}
\]
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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.