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What is the Ratio of the Volume of a Cube to that of a Sphere Which Will Fit Inside It? - Mathematics

Answer in Brief

What is the ratio of the volume of a cube to that of a sphere which will fit inside it?

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Solution

Ratio of sphere

 `=1/2 xx "side of cube"`

`r = a/2`

Now,

Volume of cube `v_1 = a^3`

Volume of sphere

`v_2 = 4/3 pir^3`

    `=4/3 pi(a/2)^3`

    `=4/3 pi a^3 / 8`

`v_2 = 1/6pia^3`

The ratio of their volumes

`v_1 :v_2 = a^3 :1/6 pia^3`

`v_1 /v_2 = a^3/(1/6 pia^3)`

      `=6/pi`

Hence, `v_1 :v_2 = 6 : pi`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 10 | Page 87
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