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Question
The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).
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Solution
Diameter of sphere curved out = side of cube = 7cm or Radius =3.5cm
Volume of cube = a3
=73
=343 cm3
Volume of sphere`=4/3pir^3`
`= 4/3 xx 22/7 xx 7/2 xx 7/2 xx 7/2 = 179.66 cm^3`
volume of the wood left=Volume of cube-volume of sphere
=343-179.66
=163.34 cm3
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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 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?
