Question 114

# A right circular cylinder has a radius of 6 and a height of 24. A rectangular solid with a square base and a height of 20, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. If water is then poured into the cylinder such that it reaches the rim, the volume of water is:

Solution

It is given that the radius of cylinder = 6 cm. The rectangular solid with a square base is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall.

Therefore, the diagonal of square base = the diameter of circular base

Hence, a$$\sqrt{2}$$ = 2*6 = 12 => a = $$6\sqrt{2}$$ cm.

The volume of water = Volume of the cylinder - Volume of the rectangular solid

$$\Rightarrow$$ $$\pi*6^2*24$$ - $$(6\sqrt{2})^2*20$$

$$\Rightarrow$$ $$864*\pi - 1440$$

$$\Rightarrow$$ $$288(3\pi - 5)$$