Question

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Answer 1

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Answer 2

Answer:

The height of the embankment is 5 m.

Step-by-step explanation:

Given : A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment.

To Find: The height of the embankment so formed?

Solution :

Dimension of well,

D=14 m, r=7 m, h=15 m

Volume of well or earth dug out

$V=\pi r^2h$

$V=\frac{22}{7}\times 7\times 7\times 15$

$V=2310$

Outer radius (R) = outer width + inner radius

R= 7+7=14m

Inner radius(r) = 7 m

Volume of embankment,

$V=\pi (R^2-r^2)\times h$

$V=\frac{22}{7}(14^2-7^2)\times h$

$V=\frac{22}{7}(196-49)\times h$

$V=\frac{22}{7}(147)\times h$

$V=462h$

Earth taken out of well is spread over all around it forming a embankment

Volume of well = Volume of embankment

$2310=462h$

$h=\frac{2310}{462}$

$h=5$

Therefore, The height of the embankment is 5 m.