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Question
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
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Solution
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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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?
