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.

**Radius r**

= [{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.**

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