In the figure, P and Q are two right cylindrical vessels each containing some water. The two vessels are placed on the same horizontal surface. The internal base radii of P and Q are in the radio 1:3. A and B are two cubes with sides in the ratio 1:2. A and B are put into P and Q respectively. Suppose both cubes are totally immersed in water without any overflow. If the rise in water level in P is 1 cm, then find the rise in level in Q.
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F.3MAth Questions
2007-03-21 3:18 am
回答 (1)
2007-03-21 4:58 am
✔ 最佳答案
side of cube A : side of cube B = 1 : 2volume of cube A : volume of cube B = 1^3 : 2^3 = 1 : 8
radius of P : radius of Q = 1 : 3
base area of P : base area of Q = 1^2 : 3^2 = 1 : 9
Since base area x height = volume
So,
base area of P x height P : base area of Q x height Q = volume of A : volume of B
(1)(1cm) : (9)(height Q) = 1 : 8
1 / (9*Height Q) = 1 / 8
Height Q = 9 / 8
Therefore, the rise in level in Q = 1.125 cm
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