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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 1 · Set 3 · Q12
(a) In Figure 2, from a solid cube of side 7 cm, a cylinder of radius 2 · 1 cm and height 7 cm is scooped out. Find the total surface area of the…
In Figure $\displaystyle 2$, from a solid cube of side $\displaystyle 7$ cm, a cylinder of radius $\displaystyle 2 \cdot 1 \mathrm{~cm}$ and height $\displaystyle 7$ cm is scooped out. Find the total surface area of the remaining solid.
Figure $\displaystyle 2$
A well of diameter $\displaystyle 5$ m is dug $\displaystyle 24$ m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width $\displaystyle 3$ m to form an embankment. Find the height of the embankment. Case Study - $\displaystyle 1$
Marking-scheme solution
(a)
Total surface area of cube \(\displaystyle =6 \times(7)^{2}-2 \times \frac{22}{7} \times 2 \cdot 1 \times 2 \cdot 1\)
\[=266 \cdot 28 \mathrm{~cm}^{2}
\]
Curved surface area of cylinder \(\displaystyle =2 \times \frac{22}{7} \times 2 \cdot 1 \times 7\)
\[=92 \cdot 4 \mathrm{~cm}^{2}
\]
Therefore surface area of remaining solid
\[\begin{aligned}
& =266 \cdot 28+92 \cdot 4 \\
& =358 \cdot 68 \mathrm{~cm}^{2}
\end{aligned}
\]
Or
\[r=2 \cdot 5 \mathrm{~m}
\]
Volume of earth dug out \(\displaystyle =\pi \times 2 \cdot 5 \times 2 \cdot 5 \times 24 \mathrm{~m}^{3}\)
Let height of embankment be \(\displaystyle h\)
\[\text { ∴ Volume of earth dug out }=\text { Volume of embankment }
\]
\[\begin{aligned}
& \Rightarrow \pi \times(2 \cdot 5)^{2} \times 24=\pi \times h\left[(5 \cdot 5)^{2}-(2 \cdot 5)^{2}\right] \\
& \quad \Rightarrow 2 \cdot 5 \times 2 \cdot 5 \times 24=h \times 8 \times 3 \\
& \quad \Rightarrow h=6 \cdot 25 \mathrm{~m}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.