A well having 10m inside diameter …

Ans. Diameter of Well = 10 m

Radius of Well = 10/2 = 5m

Depth (height) of well = 8.4 m

Volume of Well = ${22\over7} \times({5})^2 \times8.4 = {22\over7} \times25\times8.4$

= 660 m³

Volume of Well = Volume of Earth Taken Out 

=> Volume of Earth Taken Out = 660m³ .....(1)

This earth spread around well, so it ll be in form of hollow cylinder.

Let Height of Embankment = h

Inner Radius  (r) = 5m

Width of Embankment (t) = 7 m

Outer Radius (R) = r + t = 5+7 =12 m

Volume of Embankment = Volume of outer cylinder - volume of inner cylinder

=> $[{{22\over 7} \times ({R})^2\times h }] - [{{22\over7}\times ({r})^2\times h}]$

=> ${22\over7}\times h[{144-25}] ={22\over7}\times h \times 119$

=> 374h .........(2)

From (1) and (2)

=> 374h = 660

=> h = 1.765m

Rate For Digging And making embankment  = Rs. 500 per cubic meter

Actual Amount = 500 * [ Total Volume of Well + Volume Of embankment ] 

= 500*[660+660] = Rs. 660000

(as he consider height 2m)volume of embankment = 22*2*[144-25]/7= 44*119/7 = 748m³

Amount He Charged = 500* [ 660 +748 ]= 550*1408=774400

Extra money Made = 774400-660000 = Rs.114400

But madam my book answer is not match your answer.

After digging and spreading the earth, we consider the shape of hollow cylinder.

Here, Radius of well = 5 m and Outer Radius of well = 5 + 7 = 12 

Let height of embankment be h meters.

Now, Volume of Earth spread = Volume of Well

π(12)² × h = π(5)² × 8.4

h = 25 × 8.4 ÷ 144 = 1.46 m

But charge taken by contractor for 2 m height = Rs.500

Actual charge for 1.46 m height = 500/2 × 1.46 = Rs.365

Contractor charged more by Rs.500 - Rs.365 = Rs.135.