Page:Sheet Metal Drafting.djvu/57

were given and the formula $\scriptstyle {V=A\times H}$ was used. If the volume and the height were given, to find the area the volume would be divided by the height. If the volume and the area were given, to find the height the volume would be divided by the area. If the volume and the diameter were given, the preceding formula would be used first, finding the area corresponding to the given diameter.

(a)	Volume	=Area	×Height
	$\scriptstyle {V=A\times H}$
(b)	Area	=Volume	÷Height
	$\scriptstyle {A=V\div H}$
(c)	Height	=Volume	÷Area
	$\scriptstyle {H=V\div A}$

Formula (a) is the original, or basic, formula while (b) and (c) are obtained by changing the position of certain quantities.

What happens to the multiplication sign when area is carried over to the left-hand side in place of volume? Does the same thing happen when height and volume are interchanged? This process of changing the location of the terms in a formula is called transposing the formula. When any terms are transposed, the sign must also be changed to the opposite; that is, multiplication becomes division, addition becomes subtraction, and so on.

Problem 8B.—What is the area of the bottom of a garbage can 16″ high, the volume of which is 42 qts.?

Finding the Diameter of a Circle from the Area.—The formula for the area of the base of a cylinder is $\scriptstyle {A=D^{2}\times .7854}$. Problem 8B gives the area of the bottom of the can. Before the bottom can be made, its diameter must be found. There are two ways of doing this: by using printed tables giving this information; or by transposing the formula for area and finding the diameter by square root. A sheet metal worker must know how to find the square root; consequently, the student is advised to become familiar with this process.

	Original formula	$\scriptstyle {\text{Area}}$	$\scriptstyle {=D^{2}\times .7854}$
	Transposing,	$\scriptstyle {D^{2}}$	$\scriptstyle {={\text{Area}}\div .7854}$
(d)	Extracting square root,	$\scriptstyle {D}$	$\scriptstyle {={\sqrt {{\text{Area}}\div .7854}}}$