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A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

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2.5 m

3.5 m

5.5 m

6.5 m

answer is A.

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Detailed Solution

Given,
Diameter D= 7 m. Thus, the value of radius

r = 3.5 m

Now, height of the well h=20m
Earth dug out from (cylindrical) well= volume of cylinder

\begin{matrix} = π \times r \times r \times h \\ = \frac{22}{7} \times 3.5 \times 3.5 \times 20 \\ = 770 m^{3} \end{matrix}

Now,
Volume of cylinder = Volume of cuboid
770 = length × breadth × height (h)
770 = 22 × 14 × h

h = \frac{770}{22} \times 14

h = 2.5 m

Thus, the value of height is 2.5 cm.
Option 1 is correct.

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