Find the quantity of earthwork of a canal cutting

Find the quantity of earthwork of a canal cutting from chainage 30 to 90 with following details. Bed width = 10 M, Side slope 1:1.

Chainage in M	30	60	90
Depth of cutting in M	1.6	1.8	2.0

C/S at chainage 30 m.

C/S at chainage 60 m.

C/S at chainage 90 m.

C/S area for section 1

= Bd1 + Sd₁ ²

= 10 x 1.6 + 1 x 1.6²

= 18.56 m²

C/S area for section 2

= Bd2 + Sd₂ ²

= 10 x 1.8 + 1 x 1.8²

= 21,24 m²

C/S area for section 3

= Bd1 + Sd₃ ²

= 10 x 2 + 1 x 2²

= 24 m²

Total earthwork between C/S 1 and C/S 2

= Mean area x Length

= [(18.56 + 21.24) / 2] x 30

= 597 m³

Total earthwork between C/S 2 and C/S 3

= Mean area x Length

= [(21.24 + 24.00) / 2] x 30

= 678.60 m³

Therefor total earthwork between chainage

30 to 90 = 597 + 678.60

               = 12775.60 m³