Question

31. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around
it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the
embankment.
5
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Answer 1

Answer:

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

Given:

Depth (h 1) of well = 14 mRadius (r1 ) of the circular end of well = 23

m

Width of embankment = 4 m

From the figure, it can be observed that our embankment will be in a cylindrical shape having outer radius, (r 2)=4+ 23 = 211

m,

Let height of embankment be h = 2

.

Volume of soil dug from well = Volume of earth used to form the embankment

π×r12×h 1=π×(r 22−r 12 )×h 2

⟹π×( 23 ) 2×14=π×[( 211 ) 2 −( 23 ) 2×h2 ]⟹ 49 ×14= 4112 ×h2

⟹h 2 = 89

=1.125 m

So, the height of the embankment will be 1.125 m.

Answer 2

Answer:

7.87

Step-by-step explanation:

1. Volume of cylinder = πr^2h =99 Cu.m
2. Volume of circular disc using,= πr^2h
3. But this volume will be equal to the volume of embankment.
4. Therefore πr^h=99
5. Solving this equation we get h=7.87m