There is water to a height of 16 cm in a cylindrical glass jar of radius 12.5 cm. Inside the water, there is a sphere of diameter 15 cm, completely immersed. By what height will water go down, when the sphere is removed?

Given, radius of glass jar, R = 12.5 cm

Diameter of sphere = 15 cm

Radius of sphere, r = $\dfrac{\text{diameter}}{2} = \dfrac{15}{2}$ = 7.5 cm

When the sphere is removed from the jar, volume of water decreases.

Let h be the height by which water level decrease.

Volume of water decreased = Volume of sphere

$\Rightarrow π\text{R}^2\text{h} = \dfrac{4}{3}π\text{r}^3 \\[1em] \Rightarrow \text{R}^2\text{h} = \dfrac{4}{3}\text{r}^3 \\[1em] \Rightarrow \text{h} = \dfrac{4}{3} \times \dfrac{\text{r}^3}{\text{R}^2} \\[1em] \Rightarrow \text{h} = \dfrac{4}{3} \times \dfrac{7.5^3}{12.5^2} \\[1em] \Rightarrow \text{h} = \dfrac{4}{3} \times \dfrac{421.875}{156.25} \\[1em] \Rightarrow \text{h} = \dfrac{1687.5}{468.75} \\[1em] \Rightarrow \text{h} = 3.6 \text{ cm.}$

Hence, the height by which water level decrease is 3.6 cm.