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 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.
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding stimulus
Model Answer
(a)
Volume of hemispherical bowl = $\dfrac{2}{3}\pi r^3 = \dfrac{2}{3}\pi (9)^3 = \dfrac{2}{3}\pi \times 729 = 486\pi$ cm³
Volume of one cylindrical jar = $\pi r^2 h = \pi (1.5)^2 \times 4 = \pi \times 2.25 \times 4 = 9\pi$ cm³
Number of jars required $= \dfrac{486\pi}{9\pi} = \mathbf{54}$
∴ 54 cylindrical jars are required.
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(b)
The conical funnel has the same height ($h = 4$ cm) and same diameter ($r = 1.5$ cm) as the cylindrical jar.
Volume of cone $= \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 9\pi = 3\pi$ cm³
Volume of cylinder $= 9\pi$ cm³
Water that flows out = Volume of cone $= 3\pi = 3 \times \dfrac{22}{7} \approx \mathbf{9.43}$ cm³
(When the cone is immersed, it displaces a volume equal to the cone's own volume, so that much water flows out.)
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Explanation
- (a): Divide total volume of hemisphere by volume of one cylinder. Key formula: hemisphere volume = $\frac{2}{3}\pi r^3$.
- (b): A solid cone immersed in a full jar displaces water equal to its own volume = $\frac{1}{3}$ of cylinder's volume. Examiners expect the reasoning that water flowing out = volume of cone. Don't forget to show the formula and substitution clearly for full marks.