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.**

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