A well with 14 m inside diameter is dug 8 m deep. The earth taken out of it has been evenly spread a

M4maths Previous Puzzles

20 May 2016 Find the height

A well with 14 m inside diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.

OPtion

1) 49.2 cm
2) 53.3 cm
3) 61.4 cm
4) 39.6 cm
5) 32.5 cm
6) 52.6 cm
7) 46.6 cm
8) 62.3 cm
9) 58.4 cm
10)None of these

Solution

Volume of earth dug out = 22/7*7*7*8 = 1232 cm^3
Area of embankment = Pi (R^2 - r^2)
= 22/7 * (28^2 - 7^2)
= 22/7 * 35 * 21
= 2310 m^2
Therefore
Height of embankment 1232/2310 * 100 cm = 53.3 cm
Option 2)

Correct Option: 2 Best Solution (8)

rydham goyal   8 years AGO

radius of inside tank = 7m =
height = 8 m =
volume = 1231 m^3
outer radius = 7+21
= 28 m
area of embankment = area of outer circle - area of inner circle
= 2310 m^2
height of embankment = volume/area
=1231/2310
=53.3 cm

Like? Yes (46) | No (21)  

Kunal nemu   8 years AGO

given 14m diameter and 8m deep.
so radius is 7m. so volume is V = 3.141*7^2*8 =1231 m^3
find the area of whole thing minus the well.radius is 21+7=28m
area A = 3.141*28^2 - 3.141*7^2 = 2308m^2
so the height = 1231 / 2308 = 0.533m = 53.3 cm

Like? Yes (23) | No (14)  

RAHUL KUMAR   8 years AGO

vol of embankment = vol of earth taken out of it
let height of embankment = h
radius of earth or soil taken out of it = 14/2 = 7m
height of soil taken out = 8 m
then radius of well with embankment = 21 + 7 = 28m
pi * [(28)^2 - (7^2)]* h = pi * (7)^2 *8
by solving it
h = 53.33 cm
option (2)

Like? Yes (22) | No (20)  

Divesh Singla   8 years AGO

radius=diameter/2=14/2=7m
height=8m
width=21m

Volume of a cylinder = V = π x r^2 x h

volume of earth taken out = 22/7 x 7x 7 x 14 = 392m^3

Let the height of embankment be H

volume of earth used 392m^3

When you make the embankment

The volume of the of the outer cylinder - volume of the inner cylinder = volume of earth

Outer radius is Inner radius + 21m width = 28m

( π x 28 x 28 x H ) - ( π x 7 x 7 x H ) = 392

πx784xH - πx49xH = 392
735 x H = 392
H = 392 / 735pi =0.5333m^3=53.3cm

Like? Yes (19) | No (22)  

AMEER ALI KHAN   8 years AGO

volume of well = pi x 7^2 x 8 = 372pi. m^3
volume of embankment = (pi x 28^2 x h) - (pi x 7^2 x h) = 372pi m^3
so, h= 8/15 m
h= 53.3cm

Like? Yes (10) | No (14)  

Pooja Priti   8 years AGO

d=14m
h=8m
w=21m
D=d+2w=56m
H=1230.88/(3.14(784-49))=.53333m

Like? Yes (12) | No (17)  

Abdul rahiman c m k   8 years AGO

Volume of available sand from diging well = 2462 m^3

If is height of embankment then
h(2×3.14×28^2-2×3.14×7^2) =2462
On solving h=0.533 m
=53.3 cm

Like? Yes (3) | No (8)  

Bibhuti Panda   8 years AGO

Earth removed from well = Earth used to make embankment

?*7²*8=?*(28²-7²)*h
=> h = 53.333cm

Like? Yes (12) | No (24)