Question

A well with 10 m inside diameter is dug 14m deep. Earth taken out of it is spread all around it to make an embankment of height 14/3 m. The width of the embankment is________.
100 points

Answer 1

Answer:

Well with 10m diameter is dug 14m deep.

⇒ Cylindrical radius =

2

10

=5m

Volume =πr

2

h

=

7

22

×5×5×14

=1100 cubic meter

Is taken out and spread width of 5m.

( diagram )

⇒R

1

=5+5=10m

r=5m

⇒V=π(R

2

−r

2

)h

1100=

7

22

(10

2

−5

2

)h

350=(100−25)h

h=

75

350

=

3

14

⇒h=4.66m

Hence, the answer is 4.66m.

Answer 2

Radius of well = 5 m

depth = 14 m

volume of earth taken out = πr² h = π×(5)²×14= 1100 m³

now, it is spread to form embankment, which is in the form of hollow cylinder,

inner radius, r= 5 m

outer radius = 5 +5 = 10 m

height= h

then, 1100 = π×h(10²- 5²)

⇒h = 350/75 = 14/3 = 4.67 m