Question 115

# A right circular cylinder has a height of 15 and a radius of 7. A rectangular solid with a height of 12 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. The volume of the liquid is

Solution

Volume of liquid = Volume of cylinder - Volume of rectangular solid

Volume of cylinder = $$\pi*r^{2}*h$$

=$$\pi*7^{2}*15$$ = $$735\pi$$

Volume of rectangular solid = Area of square base * height

In square ABCD,  AC = $$\sqrt{2}$$*AB        so AB = $$\frac{14 }{\sqrt{2}}$$ = $$7\sqrt{2}$$

Volume of rectangular solid = Area of square base * height  = $$(AB)^{2}$$*height = $$(7\sqrt{2})^{2}*12$$

=  $$98*12$$ = $$1176$$

So Volume of liquid = Volume of cylinder - Volume of rectangular solid

= $$735\pi$$ - $$1176$$ = $$147(5π-8)$$