There is some water in a vertical cylindrical drum. A conical iron piece with a diameter of 2.8 decimeters and a height of 3 decimeters is completely submerged in the water, causing the water level to rise by 0.64 decimeters. What is the diameter of the drum?

Q.There is some water in a vertical cylindrical drum. A conical iron piece with a diameter of 2.8 decimeters and a height of 3 decimeters is completely submerged in the water, causing the water level to rise by 0.64 decimeters. What is the diameter of the drum?

Radius of the cone \(= \frac{2.8}{2}\) dm = 1.4 dm and height = 3 dm Let the radius of the drum be \(r\) dm According to the question: \(\pi r^2 \times 0.64 = \frac{1}{\cancel{3}} \pi (1.4)^2 \times \cancel{3}\) i.e., \(r^2 = \frac{(1.4)^2}{0.64}\) i.e., \(r = \frac{1.4}{0.8} = \frac{14}{8} = \frac{7}{4}\) \(\therefore\) Diameter of the drum = \(\frac{7}{4} \times 2\) dm = 3.5 dm