This line of enquiry is not only useful in solving practical construction tasks but a much-loved subject for maths puzzles in schools. Working out how much cement, or concrete, you need to fill a hole, especially when the hole is irregular in shape, takes a little bit of maths and a little bit of estimation.
Measure the longest part of the hole and call this A. Measure the widest part and call this B. Measure the deepest part and call this C. Take all measurements in metres.
Multiply the three figures together to get the maximum amount of cement, or concrete, you will need to fill the hole. For example if A = 3.53 m, B = 2.69 m and C = 0.45 m, the maximum amount of cement, or concrete you would need would be 4.27 cubic metres, to two decimal places. Call this figure D
According to mathematician Richard Elwes, one cubic metre is the volume of a cubic box 1m x 1m x 1m. Imagine a hole that is a cubic box with length equal to A, width equal to B and depth equal to C. Estimate what proportion of this cubic box your hole represents, in percentage terms. This is not as difficult as it sounds when you are standing by the hole looking into it. For example, a roughly triangular-shaped hole would be about 50 percent. A roughly circular hole would be about 75 percent, and so on. Call this estimated percentage E. Imagine E is 60 percent for the purposes of this example.
Multiply D by E. In the example previously cited, the calculation would be 4.27 x 60 percent, or (4.27 x 60) / 100. In other words, you would require 2.56 cubic metres of cement or concrete. Since you can usually only buy cement or concrete in whole units, you would round this up to 3 cubic metres.