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A 20 m deep well with diameter 7 m is dug and the earth from d

Question

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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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.

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

The shape of the well will be cylindrical as shown in the figure below:
Given:
Depth

(h)

of well

= 20

m
Radius

(r)

of circular end of well =

\frac{7}{2} m

Area of platform = Length x Breadth

= 22 \times 14

^{2}

Assume height of the platform

= H

The volume of soil dug from the well will be equal to the volume of soil scattered on the platform.
Volume of soil from well = Volume of soil used to make such platform

⟹ π r^{2} h

= Area of platform x Height of platform

⟹ π \times (\frac{7}{2})^{2} \times 20 = 22 \times 14 \times H

H = \frac{22}{7} \times \frac{49}{4} \times \frac{20}{22 \times 14}

H = \frac{5}{2} = 2.5 m

Hence, the height of such a platform will be

2.5

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Question Text	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.
Answer Type	Text solution:1
Upvotes	150

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.

Text solutionVerified

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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.