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Q.

A well of diameter 7m and 30m deep is dug and the soil obtained by digging the well is evenly spread out to form a platform of size 30m×10m. Find the height of the platform.

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a

3.85 m

b

4.85 m

c

5.85 m

d

6.85 m

answer is A.

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Detailed Solution

Concept- Use the fundamental description of volume. As we can see, earth that has been dug is also referred to if it is 7 meters in diameter and 30 meters deep, but when we look at it geometrically, it has a cylinder shape with a specific height and diameter.
The cylindrical well's diameter and depth are 30m and 7 meters.

r = \frac{d}{2} = \frac{7}{2}

For the cubical platform, the volume of dirt used to prepare the platform is equal to the following dimensions: length l = 30 m, breadth = 10 m, and height = X m.

π r^{2} h = l \times b \times h

\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 30 = 30 \times 10 \times x

x = \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{30}{30 \times 10}

x = 3.85 m

Hence, the correct answer is option 1) 3.85m

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