Multiple choice

There is a circular field of area A square metres. A cylindrical ditch of radius 14 metres and depth 5 metres is dug on the same field, and the earth is taken out and spread over the remaining part of the circular field. The height of the field goes up by 0.55 metres. The value of A is

  1. 6216

  2. 4356

  3. 5216

  4. 6316

  5. 6116
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A Correct answer
Explanation

Volume of earth taken out = pi * r^2 * depth = pi * 14^2 * 5 = 980 * pi. This volume is spread over the remaining area (A - pi * 14^2) to a height of 0.55m. So, 980 * pi = (A - 196 * pi) * 0.55. Solving for A gives A = 980 * pi / 0.55 + 196 * pi = 1781.8 * pi + 615.75 = 5600 + 615.75 = 6215.75, which rounds to 6216.

AI explanation

The volume of earth dug out is the volume of the cylindrical ditch, which is calculated as 22/7 times 14 squared times 5, equaling 3080 cubic metres. Spreading this earth over the remaining part of the circular field increases the height by 0.55 metres, meaning the base area of the remaining field is the volume divided by the height, or 3080 divided by 0.55, which is 5600 square metres. Adding the 616 square metre base area of the ditch itself (22/7 times 14 squared) to the 5600 square metres of the remaining field gives a total field area of 6216 square metres.

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