Question

Water is filled in a right cylindrical tank with base radius 14 cm, such that water
level is 3 cm below the top. When an iron ball is dropped in the tank, 3003 cm of
water flows out. Find the radius of the ball.​

Answer 1

we know that, volume of water displaced by the ball is equal to its own volume.

For the spherical ball;

volume = 3003 cm³

$\frac{4}{3}\pi {r}^{3} = 3003 \\ \frac{4}{3} \times \frac{22}{7} \times {r}^{3} = 3003 \\ \\ {r}^{3} = \frac{3003 \times 7 \times 3}{4 \times 22} = \frac{273 \times 21}{4 \times 2} \\ {r}^{3} = \frac{(3 \times 7 \times 13) \times (3 \times 7)}{8} \\ r = \sqrt[3]{ \frac{5733}{8} } \\ r = \frac{ \sqrt[3]{5733} }{2}$