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.

# 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.

1. A
3.85 m
2. B
4.85 m
3. C
5.85 m
4. D
6.85 m

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### 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.
$\pi {r}^{2}h=l×b×h$
$\frac{22}{7}×\frac{7}{2}×\frac{7}{2}×30=30×10×x$
$x=\frac{22}{7}×\frac{7}{2}×\frac{7}{2}×\frac{30}{30×10}$

Hence, the correct answer is option 1) 3.85m

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