How to Find the Volume of a Hollo Brick Chimney with Frustum Shape

In this exclusive civil engineering tutorial, you will learn how to work out the volume of any brick chimney.

A brick chimney may come with different shapes like circular, rectangular, square, elliptical and frustum and in this tutorial, detail guidelines will be provided for calculating the volume of a frustum brick chimney.

The calculation is made based on the following dimensions :-

The following formula is used to determine the volume of any solid frustum :-
h/3 (A1 + A2 + √A1A2)

Since, a hollow frustum is used in place of a solid frustum in this video, the volume will be calculated as follow :-

Volume (V) = Volume of exterior frustum – Volume of interior frustum

With formula, the above can be presented as follow :-

V = {(h/3 (A1 + A2 + √A1A2) – h/3 (a1 + a2 + √a1a2)}

As h/3 is common, the formula can be written as follow :-

V = h/3 {(A1 + A2 + √A1A2) – (a1 + a2 + √a1a2)} (here, A1,A2, a1,a2 belongs to top and bottom areas)

Here, A1 = πD12 / 4 (here D1 refers to base circle with diameter 5 m)

So, A1 = π52 / 4 = 19.634 square meter.

Also Read: Learn to work out quantities of bricks in a wall

Now, A2 = πD22 / 4 (here D2 refers to top circle with diameter 1.60 m). So, A2 = π1.602 / 4 = 2.01 square meter.

The calculation is done for inner frustum as follow :-

a1 = πd12 / 4 (here d1 refers to the base circle for the hollow frustum with diameter 4.40 meter)

So, a1 = π4.42 / 4 = 15.205 square meter

a2 = πd22 / 4 (here d2 refers to the upper top small circle with diameter 1 meter)

So, a2 = π12 / 4 = 15.205 square meter = 0.758 square meter

Now, put all the above values to the following formula :-

V = h/3 {(A1 + A2 + √A1A2) – (a1 + a2 + √a1a2)}
V = 15/3 {(19.634 + 2.01 + √19.634 x 2.01) – (15.205 + 0.785 + √15.205 x 0.785)}
V = 15/3{(27.926) – (19.445)} = 42.40 m³

So, the volume of the brick chimney = 42.40 cubic meter

Video Source: Engineer Boy