Question

A well with 10m inside diameter is 10m deep. Earth taken out of it is spread all around it to a width of 5cm to form an embankment Find the height of the embankment​

Answer 1

Answer:

20 metres is the height of the embankment

Answer 2

Given,

• Diameter of well (d) = 10 m ⇒ Radius (r) = 10/2 = 5 m

• Depth of well (h) = 10 m

We know,

$\huge{\boxed{\sf{Volume= \pi r^2 h}}}$

Applying the values to the equation:

$\sf{\implies Volume =\pi \times 5^2\times 10}$

$\sf{\implies Volume =\dfrac{22}{7} \times 5^2\times 10}$

$\sf{\implies Volume =\dfrac{22\times 25\times 10}{7}}$

$\sf{\implies Volume =\dfrac{5500}{7}}$

$\sf{\implies Volume =785.714 \ m^3}$

∵ The earth taken out and spread all around to a width of 5m embankment.

Let,

• Height of embankment = h

• Radius of embankment = R

$\sf{\implies R=5 +r}$

$\sf{\implies R=5+5}$

$\sf{\implies R=10 \ m}$

Volume of spread = Volume of cylindrical well

$\sf{\implies 785.714=\pi(R^2-r^2)h }$

$\sf{\implies h=\dfrac{785.714}{\dfrac{22}{7}(10^2-5^2)}}$

$\sf{\implies h=\dfrac{785.714\times 7}{22\times 75}}$

$\sf{\implies h=\dfrac{5500}{1650}}$

$\sf{\implies h = 3.33 \ m}$

$\boxed{\sf{\therefore Height \ of \ the \ embankment = 3.33 \ m}}$