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During rainfall, the volume of water falling in each square metre may be considered equal.i. Prove that the volume of water falling in a region is proportional to the area of the region.ii. Explain why the heights of rainwater collected in different sized hollow prisms kept near one another are equal. |
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Answer» i. The volume of water falling in each square metre are equal. Let the volume of the rain falling on the 1 square metre be k The volume of the rain falling on the 2 square metre = 2k The volume of the rain falling on the 3 square metre = 3k The volume of the rain falling on the x square metre y = kx Here x and y are proportional. ii. Let x be the base area of the vessel and h be the height of the water collected, then the volume of water y = xh. y/x =h The volume of water collected is different in hollow prisms having different base area. But \(\frac{volume}{Area}\) is always equal to the height of water level. So the height at which rainwater collected is same. |
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