# A Well with 10 M Inside Diameter is Dug 8.4 M Deep. Earth Taken Out of It is Spread All Around It to a Width of 7.5 M to Form an Embankment. Find the Height of the Embankment. - Mathematics

A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.

#### Solution

r = 10/2

 = 5m

Depth of well h = 8.4 m

Clearly,

Volume of earth dugout

= pi(5)^2 xx 8.4

= pi xx 25 xx 8.4

 =(22 xx 25 xx 8.4)/7 m^3

Let h' be the height of embankment

Clearly,

Embankment forms a cylindrical shell whose inner and outer radius are 5 m and 12.5 m respectively.

∴ Volume of the embankment

= pi{(12.5)^2 - (5)^2} xx h

= pi xx 17.5 xx 7.5 xx h' m^3

But, volume of earth dugout = volume of the embankment

(22 xx 25 xx 8.4)/7 = 22/7 xx 17.5 xx 7.5 xx h

h = (25 xx 8.4)/(17.5 xx 7.5)

h = 1.6 m

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 4 | Page 81