Question

A well of diameter 4m is dug 14m deep. the earth taken out is spread evenly all around the well to form a 40cm high embankment . Find the width of the embankment......in this hoe to find the volume of the embankment?

Answer 1

Answer of the given question...

Answer 2

Answer:

10 m

Step-by-step explanation:

Diameter of well = 4m = 400 cm

Radius of well r  = $\frac{400}{2} = 200 cm$

Depth of well = 14 m = 1400 cm

Volume of well = $\pi r^{2} h$

                          = $\frac{22}{7} \times 200^2 \times 1400$

Since we are given that the earth taken out is spread evenly all around the well to form a 40 cm high embankment . So, volume of well = Volume of embankment

Let the outer radius be R  

So, radius of embankment = radius of well +width = 200 +x

Volume of embankment = $\pi (R^2-r^{2}) h$

                                       = $\frac{22}{7} \times  (R^2-200^{2}) \times 40$

So,$\frac{22}{7} \times 200^2 \times 1400=\frac{22}{7} \times  (R^2-200^{2}) \times 40$

$56000000= (R^2-200^{2}) \times 40$

$\frac{56000000}{40}= (R^2-200^{2})$

$1400000= (R^2-40000)$

$1400000 +40000 = (R^2)$

$1440000 = (R^2)$

$\sqrt{1440000} = R$

$1200= R$

Thus outer radius = 1200 cm

Width = Outer radius - Inner radius = 1200-200 = 1000 cm = 10 m.

Hence the width of the embankment is 10 m.