How much dirt is in a hole that is 8 feet in diameter and 28 inches deep hold?

Answer 1

A hole in itself contains no dirt otherwise it wouldn't be a hole, but I presume you mean how much dirt has been extracted to make a hole 8ft in diameter and 28 inches deep (or how much dirt is needed to fill such a hole).

Assuming the hole has a circular cross section and is thus a cylinder, you need to know the volume of a cylinder, which is the area of the circular end times its length, namely V = pi x r2 x h.

The radius of a circle is half its diameter, so the radius r of the hole is 8' / 2 = 4'.

The height of the hole is 28".

Before the formula can be used, the units have to be all the same, in this case either feet or inches.

Converting to inches: the radius of 4ft converted to inches would be 4ft x 12 = 48in.

So the volume of dirt required to fill the hole would be:

v = pi x 482 x 28 cu in ~= 3.14 x 482 x 28 cu in ~= 202670 cu in.

Alternatively, converting to feet: the depth of 28 in converted to feet would be 28in / 12 ~= 2.33ft So the volume of dirt required to fill the hole would be:

v = pi x 42 x 2.33 cu ft ~= 117.3 cu ft.

It is also possible to convert the answer directly between cu in and cu ft by noting that 1 foot equals 12 inches and so 1 cu ft is 1ft x 1ft x 1ft = 12in x 12in x 12in = 1728 cu in.

Thus to convert cu in to cu ft, divide by 1728, so 202670 cu in / 1728 ~= 117.3 cu ft.