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Mathematics

If a sphere just fits in a right circular cylinder, then the ratio of the volume of sphere to the volume of the cylinder is :

  1. 1 : 3

  2. 1 : 2

  3. 2 : 3

  4. 1 : 4

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Answer

Let r be the radius of the sphere

If a sphere just fits in a right circular cylinder, then the ratio of the volume of sphere to the volume of the cylinder is. Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

The radius of cylinder is also r cm and height of the cylinder is 2r cm

By formula,

Volume of cylinder = πr2h

= πr2(2r)

= 2πr3

By formula,

Volume of sphere = 43π×r3\dfrac{4}{3}π \times \text{r}^3

Ratio of the volume of sphere to the volume of the cylinder:

=43π×r32π×r3=43×12=46=23= \dfrac{\dfrac{4}{3}π \times \text{r}^3}{2π \times \text{r}^3} \\[1em] = \dfrac{4}{3} \times \dfrac{1}{2} \\[1em] = \dfrac{4}{6} \\[1em] = \dfrac{2}{3}

Hence, option 3 is the correct option.

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