Question

A well of diameter 2 m dug 14 m deep. The earth taken out of it is spread evenly all around it to form an embankment of height 40 cm. Find the width of the embankment.

Answer 1

Heya mate, Here is ur answer

This orange figure =hollow cylinder u can see is the embankment of a well.


Shape of well = cylinder

Volume of earth dug out = π r^2 h

Given that well is 2 m in diameter, so radius =2/2

=1 m

Height=14 m

Volume of earth taken out= πr^2h

$= \frac{22}{7} \times 1 \times 1 \times 14$

=44m ^3

Shape of embankment= hollow cylinder

Height(H)=40 cm

=40/100 m

=0.4 m

Let Bigger Radius be r2.

Volume of embankment=π(r2^2-r^2)×H

$= \frac{22}{7} \times (r2 {}^{2} - 1 {}^{2} ) \times 0.4$

Volume of embankment= Volume of earth taken out

$\frac{22}{7} \times ({r2}^{2} - 1) \times 0.4 = 44$

$(r2 {}^{2} - 1) = \frac{44 \times 7}{22 \times 0.4}$

$r2 {}^{2} - 1 = 35$

$r2 {}^{2} = 35 + 1$

$r2 {}^{2} = 36$

$r2 = \sqrt{36}$

$r2 = 6 \: \: m$

So, width of the embankment= r2-r

=6-1

=5 m

Warm regards

@Laughterqueen

Be Brainly✌✌

Answer 2

$\underline \bold {Solution:-}$

Diameter of well = 2 m

Radius of well = 1 m

Depth of well = 14 m

Volume of mud dug out from the well

$= \pi \times {(radius)}^{2} \times depth \\ \\ = \pi \times {1}^{2} \times 14 \\ \\ = 14\pi \: {m}^{3}$

That mud is spreaded all around it in the form of a circular ring to form the embankment .

Height of mud = 40cm = 0.4 m

Internal radius of embankment = 1m

Let outer radius of embankment be r.

Volume of embankment = Volume of mud digged out

$\pi {( {r}^{2} - {1}^{2}) } \times 0.4 = 14\pi \\ \\ {( {r}^{2} - {1}^{2}) } = \frac{14\pi}{0.4\pi} \\ \\ {( {r}^{2} - {1}) } = 35 \\ \\ {r}^{2} = 36 \\ \\ r = 6$

So ,

the width of the embankment

= Outer radius- inner radius

= 6 - 1

= 5 metre