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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 4 · Set 2 · Q13
Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted…
Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea-sets, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as 'The Ceramic Town'. One of the private schools of Bulandshahr organised an Educational Tour for class $\displaystyle 10$ students to Khurja. Students were very excited about the trip. Following are the few pottery objects of Khurja.
Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. Maths teacher who was accompanying the students asked following questions :
(a)
The internal radius of hemispherical bowl (filled completely with water) in I is $\displaystyle 9$ cm and radius and height of cylindrical jar in II is $\displaystyle 1.5$ cm and $\displaystyle 4$ cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required ?
(b)
If in the cylindrical jar full of water, a conical funnel of same height and same diameter is immersed, then how much water will flow out of the jar ? Case Study - $\displaystyle 2$
Marking-scheme solution
(a)
Cylinder- $\displaystyle h=4 \mathrm{~cm}, r=1 \cdot 5 \mathrm{~cm}=\frac{3}{2} \mathrm{~cm}$
\[\begin{aligned}
\text { Volume of cylinder } & =\pi r^{2} h \\
& =\pi \times(1.5)^{2} \times 4 c m^{3}
\end{aligned}
\]
Radius of hemisphere $\displaystyle R=9 \mathrm{~cm}$
\[\begin{aligned}
\text { Volume of hemisphere } & =\frac{2}{3} \pi R^{3} \\
& =\frac{2}{3} \times \pi \times(9)^{3} \mathrm{~cm}^{3}
\end{aligned}
\]
Let the number of cylindrical jars be $\displaystyle n$
\[\therefore n \times \pi \times(1.5)^{2} \times 4=\frac{2}{3} \times \pi \times(9)^{3}
\]
\[\Rightarrow \mathrm{n}=\frac{9 \times 9 \times 9 \times 2}{4 \times 1.5 \times 1.5 \times 3}=54
\]
∴ Number of cylindrical jars required = $\displaystyle 54$
(b)
For conical funnel, $\displaystyle r=\frac{3}{2} c m, h=4 c m$
∴ Volume of conical funnel $\displaystyle =\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times \frac{22}{7} \times \frac{3}{2} \times \frac{3}{2} \times 4$
\[=\frac{66}{7} \mathrm{~cm}^{3} \text { of water will flow out. }
\]
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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.