Question

Lead sphere of diameter 6cm are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is 18 cm and the rise in the level of water is 40cm. The number lead sphere dropped in the water is

Answer 1

Let no. of lead spheres dropped in water be n. Then, A/Q
volume of water rise = n*volume of a sphere
$\pi r {}^{2} h = \frac{4}{3} \pi \: r {}^{3}$
${9}^{2} \times 40 = n \times \frac{4}{3} \times 3 \times 3 \times 3$
$81 \times 40 = 36n$
$n = \frac{81 \times40}{36}$
$n = 90$
Hence, no. of lead spheres dropped in water is 90