### How to calculate the length & volume of a semi-circular arch?

Let us now calculate the length & volume of the semi-circular arch as shown below.

Given data:

The span of the semi-circular arch = 2m.

Height of arch = 1m.

Width of the arch = 300mm.= 0.3m.

Thickness of the arch = 230mm = 0.23m.

First, we will calculate the length of the arch

The arch length is calculated by the formula

=[ ∅ × (2πr ÷ 360°)]

Here,

∅ = angle formed by the arch as shown below.

For a semi-circular arch, the value of = 180°

r = Radius of the arch.

To calculate the volume of the arch, let us calculate the radius of the centerline as shown below.

= [{arch span + (half of the arch width on both sides.)}÷ 2 ]

= [{2m. + ( 2nos.×0.5 × 0.3m.)} ÷ 2]

= [{2m. + ( 0.3m.)} ÷ 2]

= [2.3m ÷ 2]

r  = 1.15m.

1.   The arch length

=[ ∅ × {(2πr) ÷ 360°}]

=[180° × {(2 × 3.142 × 1.15)÷ 360°}]

=[180° × {7.227÷ 360°}]

(By cancelling 180° & 360° with each other)

= [ 7.227 ÷ 2 ]

= 3.613m.

Now,

2. The volume of the semi-circular arch

= [length × breadth × thickness]

= [3.613m. × 0.3m. × 0.23m.]

=0.249 CUM.