Question

a well of inner diameter 14cm is dug to adepth of 12 cm ,earth taken out of it has been evenly spread all around into a width of 7cm to form an embankment find the height of embankment​

Answer 1

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.

Answer 2

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Given:

A well of inner diameter 14cm is dug to a depth of 12cm, earth taken out of it has been evenly spread all around into a width of 7cm to form an embankment.

To find:

The height of embankment.

Explanation:

We have,

• Inner diameter of well= 14cm
• Radius of well,r= 14/2= 7cm
• Depth of dug well,h= 12cm

We know that volume of the cylinder: πr²h    [cubic units]

Volume of the earth dug out= $(\frac{22}{7} *7*7*12)cm^{3}$

Volume of the earth dug out= $(\frac{22}{\cancel{7}} *\cancel{7}*7*12)cm^{3}$

Volume of the earth dug out= (22× 7× 12)cm³

Volume of the earth dug out= 1848cm³

&

Given,

Width of the embankment= 7cm

∴ Total radius= 7cm+7cm

Total radius,R= 14cm.

Now,

Volume of embankment= Total volume - Inner volume

Volume of embankment= πR²h - πr²h

Volume of embankment= πh(R² - r²)

Volume of embankment= πh(14² - 7²)

Volume of embankment= πh(196 -49)

Volume of embankment= πh(147)

Volume of embankment= $\frac{22}{\cancel{7}}*h*\cancel{147}$

Volume of embankment= (22 *21)h cm³

Volume of embankment= 462h cm³

Now,

Volume of embankment = volume of earth dug out

→ 462h cm³ = 1848cm³

→ h= $\frac{\cancel{1848}}{\cancel{462}}$

→ h= 4cm.

Thus,

The height of embankment is 4cm.