# PARAM VISIONS

All about civil construction knowledge- PARAM VISIONS

### How to calculate the surface area & volume of stone pitching quadrant?

Let us calculate the surface area of the stone pitching quadrant as shown below.

As you can observe in the above diagram, the stone pitching covers the quadrantal surface area of a cone.

i.e. 1/4th the lateral surface area of a cone.

Now, the lateral surface area of the cone is calculated by the formula  = πrl

Where,

l = taper length.

r = radius of the cone.

h = height of the cone.

Let us observe the detailed drawing of the stone pitching as shown below.

Given data:

Height of the stone pitching = h = 1.7m.

The radius of the pitching quadrant = r = 2.2m.

The thickness of stone pitching = 300mm. = 0.3m.

Calculation:

The surface area of stone pitching

= [1/4th the lateral surface of a cone]

= [1/4 х πrl]

Here,

l² = [r² + h²]

(By Pythagoras' theorem.)

l = [√ (r² + h²)]

=  [√ (2.2² + 1.7²)]

= [√ (4.84+ 2.89)]

l  = [ √ 7.73]

l = 2.78m.

The surface area of stone pitching

= [1/4 х πrl]

= [1/4 х 3.142 х 2.2 х 2.78]

= 4.804 m²

The volume of stone pitching

= [ surface area  х thickness of pitching]

= [ 4.804m²  х 0.3m.]

= 1.441 m³

Thank you for going through these calculation steps. Have a good day 😄.