Question

Pavan filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 0.7 cm. Find the height the water will be raised to when the spherical ball is dropped into it?

• A. $0.93\times {10}^{-2}\text{cm}$
• B. $0.5\times {10}^{-2}\text{cm}$
• C. $0.6\times {10}^{-2}\text{cm}$
• D. $0.93\times {10}^{-2}\text{cm}$

Answer 1

The correct option is A $0.93\times {10}^{-2}\text{cm}$

Given, Solid: Cylindrical Vessel
Height of cylinder, $h=14\text{cm}$
Radius of Cylinder, $R=7\text{cm}$
Solid: Spherical Ball
Radius, $r=0.7\text{cm}$

Water that will flow out will be equal to the volume of spherical ball dropped into the conical vessel.

Let height ot be raised be, $h_r$

So, $\frac{4}{3}\pi r^3=\pi R^2{h}_r\frac{4}{3}{r}^3=R^2{h}_r\frac{4}{3}(0.7{)}^3=7^2\times h_{r}49h_r=\frac{4}{3}\times (0.7{)}^3{h}_r=\frac{4}{3}\times \frac{0.49\times 0.7}{49}{h}_r=0.933333\times 0.01\text{cm}{h}_r=0.93\times {10}^{-2}\text{cm}$

The hight of water in vessel will be raised by $0.93\times {10}^{-2}\text{cm}$