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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 1 · Set 2 · Q12
(a) From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the total surface…
(a)
From a solid cylinder of height $\displaystyle 30$ cm and radius $\displaystyle 7$ cm, a conical cavity of height $\displaystyle 24$ cm and same radius is hollowed out. Find the total surface area of the remaining solid.
OR
(b)
Water in a canal, $\displaystyle 8$ m wide and $\displaystyle 6$ m deep, is flowing with a speed of $\displaystyle 12$ km/hour. How much area will it irrigate in one hour, if $\displaystyle 0.05$ m of standing water is required ? Case Study - $\displaystyle 1$
Marking-scheme solution
\[l=\sqrt{576+49}=25 \mathrm{~cm}
\]
\[\begin{aligned}
\mathrm{TSA} & =2 \pi r h+\pi r^{2}+\pi r l \\
& =\frac{22}{7} \times 7[60+7+25] \\
& =2024 \mathrm{~cm}^{2}
\end{aligned}
\]OrDistance covered by water in $\displaystyle 1 \mathrm{hr}=12000 \mathrm{~m}$
∴ Volume of water flown in $\displaystyle 1$ hr
\[=8 \times 6 \times 12000 \mathrm{~m}^{3}
\]Hence area of field $\displaystyle \times 0 \cdot 05=8 \times 6 \times 12000$
\[\Rightarrow \quad \text { Area of field }=1152 \times 10^{4} \mathrm{~m}^{2} \text { or } 11520000 \mathrm{~m}^{2}
\]
\[\begin{aligned}
\mathrm{TSA} & =2 \pi r h+\pi r^{2}+\pi r l \\
& =\frac{22}{7} \times 7[60+7+25] \\
& =2024 \mathrm{~cm}^{2}
\end{aligned}
\]OrDistance covered by water in $\displaystyle 1 \mathrm{hr}=12000 \mathrm{~m}$
∴ Volume of water flown in $\displaystyle 1$ hr
\[=8 \times 6 \times 12000 \mathrm{~m}^{3}
\]Hence area of field $\displaystyle \times 0 \cdot 05=8 \times 6 \times 12000$
\[\Rightarrow \quad \text { Area of field }=1152 \times 10^{4} \mathrm{~m}^{2} \text { or } 11520000 \mathrm{~m}^{2}
\]All Surface Areas and Volumes questions2022 question paperNCERT solutions: Surface Areas and VolumesPractice Surface Areas and Volumes →
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