Question

When a metallic ball bearing is placed inside a cylindrical container, of radius $2$ cm, the height of the water, inside the container, increases by $0.6$ cm. The radius to the nearest tenth of a centimeter, of the ball bearing is

• A. $1.2cm$
• B. $1.5cm$
• C. $1.9cm$
• D. $1.6cm$

Answer 1

The correct option is A $1.2cm$

When a metallic ball bearing is placed inside a cylindrical container of radius $2cm,$ the height of the water inside the container increased by $0.6cm.$

Hence, the volume of the metallic ball is equal to the volume of water displaced,

$V=\pi r^{2}h$

$\Rightarrow$ $V=\pi \times (2{)}^2\times (0.06)$

$=2.4\pi$

Hence, the radius of the sphere is simple,

$\Rightarrow$ $\frac{4}{3}\pi R^3=2.4\pi$

$\Rightarrow$ $R^3=\frac{7.2}{4}$

$\Rightarrow$ $R^3=1.8$

$\Rightarrow$ $R=1.21\approx 1.2cm$