Question

A well of inner diameter 14metre is dug to a depth of 12metre. Earth taken out of it has evenly spread all around it to a width of 7metre to form an embankment. Find the height of the embankment. ​

Answer 1

r of well = 14 ÷ 2= 7 m

h of well (depth) = 12m

R of embankment= r + 7 = 7+ 7= 14 m

H is the height of the embankment

Volume of earth taken out from the well = volume of earth used for embankment

i.e, pie r^2 h = pie R^2 H - pie r^2 H

= pie H (R^2 -r^2)

r^2 h = H (R+r)(R-r)

(7)^2 × 12 = H (14+12)(14-12)

49 × 12 = H (26)(2)

H = 49×12 ÷ 26×2

= 11.3

Thus the height of the embankment is 11.3 m

Hope it helped......