# PARAM VISIONS

All about civil construction knowledge- PARAM VISIONS

### How to calculate the concrete volume of slump cone?

The volume of the slump cone is calculated by the formula

= [ (h ÷ 3 ) ×{ A1+A2 + √A1× A2 }]

Where

h = height of the slump cone.

A1 = area of the top circular surface.

A2 = area of the bottom circular surface.

Given data:

Height of the slump cone h = 300mm.=0.3m

Diameter of the top surface d1 = 100mm.=0.1m.

Diameter of the bottom surface d2 = 200mm.=0.2m

First, we will calculate the area A1 & A2

A1 = [( π ×  d12) ÷ 4]

=  [( 3.142 ×  0.12) ÷ 4]

=  [0.03412 ÷ 4]

= 0.007855 sqm.

A2=  [( π ×  d22) ÷ 4]

=  [( 3.142 ×  0.22) ÷ 4]

=  [0.12568 ÷ 4]

= 0.03142 sqm.

The volume of slump cone

= [ (h ÷ 3 ) ×{ A1+A2 + √A1× A2 }]

= [ (0.3 ÷ 3 ) ×{ 0.007855+0.03142 + √0.007855× 0.03142 }]

= [ (0.1) ×{ 0.039275 + √0.0002468 }]

= [ (0.1) ×{ 0.039275 + 0.01571}]

=[ 0.1  × 0.054985]

=0.00549 cu m.

= 0.1939 cu ft.

Alternate method:

Volume of the slump cone

= [ ( π × h ÷ 3) × { r12 +r1 × r2  +  r22 }]

Where, r1 = radius of top circular surface.

r2 = radius of bottom circular surface.

h = height of the slump cone.

Here,

r1 = d1 ÷ 2

= 0.1÷ 2 =0.05m.

r2 = d2 ÷ 2

= 0.2÷ 2 =0.1m.

The volume of slump cone

= [ ( π × h ÷ 3) × { r12 +r1 × r2  +  r22 }]

= [ ( 3.142× 0.3 ÷ 3) × { 0.052 + 0.05 × 0.1  +  0.12 }]

= [(0.3142) × { 0.0025 + 0.005 + 0.01}]

= [ 0.3142 × 0.0175]

= 0.00549 cu m.

= 0.1939 cu ft.