A right circular cylinder is partially filled with water. Two iron spherical balls are completely immersed in the water so that the height of the water in the cylinder rises by 4 cm. If the radius of one ball is half of the other and the diameter of the cylinder is 18 cm, then the radii of the spherical balls are

Answer: Option C

Solution

Answer: Option C

Solution:

Total volume of 2 balls = volume of cylinder of height = 4 cm
$$\begin{array}{rl}& \frac{4}{3}\pi r_1^3+\frac{4}{3}\pi r_2^3=\pi 9^2\times 4\\ & r_1=2r_2\left(\text{given}\right)\\ & \frac{4}{3}\pi \left(8r_2^3+r_2^3\right)=\pi \times 9\times 9\times 4\\ & 9r_2^3=9\times 9\times 3\\ & r_2=3\\ & r_1=2r_2=2\times 3=6\end{array}$$