Question 56

Ratio of the volumes of a sphere of radius 'r' and a cylinder of radius 'r' and height '2r' is:

Solution

Given,

Radius of sphere = r

Radius of cylinder = r and its height = 2r.

Ratio of formula for volume of sphere and cylinder is,

$${\frac{4}{3}}\times{π}{r^3}$$ : $${π}{r^2}{h}$$

substituting r and h values in the formula,

$${\frac{4}{3}}\times{π}{r^3}$$ : $${π}{r^2}{2r}$$

$${\frac{4}{3}}\times{r^3}$$ : $${2}{r^3}$$

$$\frac{4}{3}$$ : $${2}$$

$${4}$$ : $${6}$$

$${2}$$ : $${3}$$

Therefore the answer is 2:3

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