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प्रश्न
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension 6cm \[\times\] 42cm \[\times\] 21 cm.
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उत्तर
The dimensions of the solid rectangular lead piece is
\[66 cm \times 42 cm \times 21 cm\].
Diameter of the spherical lead shots = 4.2 cm Let n spherical lead shots be obtained from the rectangular piece.
\[n \times\text { volume of spherical lead shot = Volume of the rectangular lead piece}\]
\[ \Rightarrow \frac{\text { Volume of the rectangular lead piece}}{\text { volume of spherical lead shot}} = n\]
\[ \Rightarrow \frac{66 \times 42 \times 21}{\frac{4}{3} \pi r^3} = n\]
\[ \Rightarrow \frac{66 \times 42 \times 21}{\mathit{\frac{4}{3}\pi \left( \frac{4 . 2}{2} \right)^3}} = n\]
\[ \Rightarrow \frac{58212}{38 . 808} = n\]
\[ \Rightarrow n = 1500\]
Hence, 1500 lead shots can be formed.
DISCLAIMER: There is some error in the question given. Instead of 6 cm, there should be 66 cm.
The result obtained is by taking 66 cm as the dimensions of the rectangular piece.
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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. |
Maths teacher who was accompanying the students asked the following questions:
- The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and the radius and height of the cylindrical jar in II are 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?
- If in the cylindrical jar full of water, a conical funnel of the same height and same diameter is immersed, then how much water will flow out of the jar?
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
Length of the cylindrical part is 7 m and radius of cylindrical part is `7/2` m.
Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m2 of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m2.
