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If a Sphere is Inscribed in a Cube, Then the Ratio of the Volume of the Sphere to the Volume of the Cube is - Mathematics

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प्रश्न

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is

विकल्प

  •  π : 2

  •  π : 3

  • π : 4

  • π : 6

MCQ
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उत्तर

In the given problem, we are given a sphere inscribed in a cube. So, here we need to find the ratio between the volume of a sphere and volume of a cube. This means that the diameter of the sphere will be equal to the side of the cube. Let us take the diameter as d.

Here,

Volume of a sphere (V1) `(4/3) pi (d/2)^3`

` = (4/3)pi(d^3/8)`

=`(pi d^3)/6`

Volume of a cube (V2) = S

`=d^3`

Now, the ratio of the volume of sphere to the volume of the cube =  `V_1/V_2`

`V_1/V_2=(((pi d^3)/6))/d^3`

So, the ratio of the volume of sphere to the volume of the cube is  π : 6

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अध्याय 21: Surface Areas and Volume of a Sphere - Exercise 21.4 [पृष्ठ २७]

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आरडी शर्मा Mathematics [English] Class 9
अध्याय 21 Surface Areas and Volume of a Sphere
Exercise 21.4 | Q 10 | पृष्ठ २७

वीडियो ट्यूटोरियलVIEW ALL [2]

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