Multiple choice

Rain water which falls on a flat rectangular surface of length 6m and breadth 4m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if there is a rainfall of 1cm?

  1. 83.2 cm

  2. 106.4 cm

  3. 124.6 cm

  4. 190.9 cm
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D Correct answer
Explanation

Volume of water = 600cm * 400cm * 1cm = 240,000 cm^3. Cylinder volume = pi * r^2 * h. 240,000 = 3.14 * 20^2 * h. h = 240,000 / (3.14 * 400) = 240,000 / 1256 = 191.07 cm (approx 190.9).

AI explanation

The volume of rainwater is the volume of a rectangular prism with length 600 cm, breadth 400 cm, and height 1 cm, which equals 240000 cubic cm. This volume is transferred to a cylinder with a radius of 20 cm, so using the cylinder volume formula V = πr²h gives 240000 = (22/7) × 20² × h. Solving for h yields h = 190.9 cm.

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