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 teac

Question

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 teacups, 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.

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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 9 cm and radius and height of cylindrical jar in II is 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required?

Accepted Answer

Step 1: Cylinder: $h = 4$ cm, $r = 1.5$ cm $= \frac{3}{2}$ cm
Volume of cylinder $= \pi r^2 h$
$= \pi 	imes (1.5)^2 	imes 4$ cm$^3$
Step 2: Radius of hemisphere $R = 9$ cm
Volume of hemisphere $= \frac{2}{3}\pi R^3$
$= \frac{2}{3} 	imes \pi 	imes (9)^3$ cm$^3$
Step 3: Let the number of cylindrical jars be $n$
$	herefore n 	imes \pi 	imes (1.5)^2 	imes 4 = \frac{2}{3} 	imes \pi 	imes (9)^3$
Step 4: $\Rightarrow n = \frac{9 	imes 9 	imes 9 	imes 2}{4 	imes 1.5 	imes 1.5 	imes 3} = 54$
$	herefore$ Number of cylindrical jars required $= 54$

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