The radii of the base of two cylindrical tins, P and Q are r and 2r respectively. If the water level in p is 10cm high, would be the height of the same quan...

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height of the cylinder. The volume of the water in tin P is V_P = πr²h_P, where r is the radius of the base of tin P and h_P is the height of the water in tin P. The volume of the same quantity of water in tin Q is V_Q = π(2r)²h_Q = 4πr²h_Q, where 2r is the radius of the base of tin Q and h_Q is the height of the water in tin Q. Since the same quantity of water is in both tins, V_P = V_Q. Substituting the expression for V_P and V_Q into the equation V_P = V_Q gives πr²h_P = 4πr²h_Q, which simplifies to h_Q = h_P/4. Therefore, the height of the water in tin Q is one-fourth of the height of the water in tin P. Since the height of the water in tin P is 10cm, the height of the water in tin Q would be (10/4) cm = 2.5 cm. Therefore, the height of the same quantity of water in tin Q is 2.5 cm. Answer option (A) is the correct answer.