A vertical cylindrical drum with a radius of 21 cm and height of 21 cm is completely filled with water. A solid sphere with a radius of 21 cm is taken and fully submerged into the drum, then removed. As a result, what is the new depth of water in the drum?

Q.A vertical cylindrical drum with a radius of 21 cm and height of 21 cm is completely filled with water. A solid sphere with a radius of 21 cm is taken and fully submerged into the drum, then removed. As a result, what is the new depth of water in the drum?

Volume of water in the cylindrical drum = \( \pi \times 21^2 \times 21 \) cubic cm = \( \pi \times 21^3 \) cubic cm Since both the radius of the sphere and the height of the drum are 21 cm, the sphere will be half-submerged. So, the volume of water displaced = \( \frac{2}{3} \pi \times 21^3 \) cubic cm ∴ Remaining volume of water = \( \pi \times 21^3 - \frac{2}{3} \pi \times 21^3 \) cubic cm = \( \frac{1}{3} \pi \times 21^3 \) cubic cm Let the new depth of water in the drum be \( h \) cm ∴ \( \pi \times 21^2 \times h = \frac{1}{3} \pi \times 21^3 \) i.e., \( h = \frac{21}{3} = 7 \) ∴ The new depth of water in the drum is 7 cm.