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प्रश्न
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
उत्तर
Let the radius of the shere be R and the edge of the cube be a.
As the sphere is fit inside the cube .
so, diameter of the sphere =edge of the cube
⇒ 2R = a ...........(i)
Now,
The ratio of the cube to that of the sphere`= "Volume of the cube"/"Volume of the sphere"`
`=a^3/((4/3pi"R"^3))`
`=(2"R")^3/((3/4pi"R"^3))` [Using (i)]
`=(3xx8"R"^3)/(4pi"R"^3)`
`=6/pi`
`=6 : pi`
so,the ratio of the Volume of the cube to that of the sphere is 6 : π.
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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?
