Question 106

The volumes of a right circular cylinder and a sphere are equal. The radius of the cylinder and the diameter of the sphere are equal. The ratio of height and radius of the cylinder is

Solution

Let the radius and height of right circular cylinder be r and h respectively.

Let radius of sphere is R.

The radius of the cylinder and the diameter of the sphere are equal.

Therefore, r = 2R

The volumes of a right circular cylinder and a sphere are equal.

=> $$\pi r^2h = \frac{4}{3} \pi R^3$$

=> $$3 r^2h = 4(\frac{r}{2})^3$$

=> $$6 r^2h = r^3$$

=> $$6h = r$$

=> $$\frac{h}{r} = \frac{1}{6}$$

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