A tank measuring 21 decimeters in length, 11 decimeters in width, and 6 decimeters in depth is half-filled with water. If 100 solid spheres, each with a diameter of 21 centimeters, are submerged into the tank, by how many decimeters will the water level rise?

Q.A tank measuring 21 decimeters in length, 11 decimeters in width, and 6 decimeters in depth is half-filled with water. If 100 solid spheres, each with a diameter of 21 centimeters, are submerged into the tank, by how many decimeters will the water level rise?

The radius of each iron sphere = \(\cfrac{21}{2}\) cm \(= \cfrac{21}{2 \times 10} = \cfrac{21}{20}\) decimeters Volume of 100 iron spheres = \(100 \times \cfrac{4}{3} \pi \left(\cfrac{21}{20}\right)^3\) cubic decimeters \(= 100 \times \cfrac{4}{3} \times \cfrac{22}{7} \times \cfrac{21 \times 21 \times 21}{20 \times 20 \times 20}\) cubic decimeters \(= 485.1\) cubic decimeters Let the water level rise by \(h\) decimeters. According to the question, \(21 \times 11 \times h = 485.1\) ⇒ \(h = \cfrac{485.1}{21 \times 11} = 2.1\) ∴ The water level in the tank will rise by 2.1 decimeters.