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.
Calculation:
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 the 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:
The 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 the 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.
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Thank you for going through these calculation steps❤. Have a good day 😄.
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