a well whose diameter is 7m has been dug 22.5m deep and the earth dugout is used to form an embankment around it. if the height of the embankment is 1.5m find the width of the embankment
Answers
Answer:
the width of embankment will also be equal to the width of well
Answer:
The diameter of the well dug out is 7m and its height is 22.5m.
We know that the radius of the circle is half the diameter of the circle. So, the radius of cylinder =72=3.5m
=72=3.5m
.
We know that the volume of a cylindrical vessel whose radius is ‘r’ and height is ‘h’ is given by πr2h
πr2h
.
Substituting r=3.5m,h=22.5m
r=3.5m,h=22.5m
in the above formula, the volume of well dug out =πr2h=227(3.5)2(22.5)=866.25m3
=πr2h=227(3.5)2(22.5)=866.25m3
.
This volume of earth is equal to the volume of earth used to make embankments.
Let’s assume that the width of the embankment is ‘x’.
So, the outer radius of embankment is (x+3.5)m
(x+3.5)m
, inner radius is 3.5m and height is 1.5m.
To calculate the volume of earth used to make embankment, we will use the formula π(R2−r2)h
π(R2−r2)h
, where R is outer radius, r is inner radius and h is the height of embankment.
Substituting the values, the volume of embankment =π((x+3.5)2−3.52)1.5
=π((x+3.5)2−3.52)1.5
.
Thus, we have 866.25=π((x+3.5)2−3.52)1.5
866.25=π((x+3.5)2−3.52)1.5
.
Simplifying the above equation, we have 183.75=(x+3.5)2−12.25
183.75=(x+3.5)2−12.25
.
Thus, we have (x+3.5)2=183.75+12.25=196
(x+3.5)2=183.75+12.25=196
.
So, we have x+3.5=196−−−√=14⇒x=14−3.5=10.5m
x+3.5=196=14⇒x=14−3.5=10.5m
.
Hence, the width of the embankment is 10.5m.
