Question 507817
The formula:
{{{V = (1/3)l*w*h}}} Relates to any "rectangular" pyramid, of which, a "square" pyramid is an example.
To say "square" pyramid implies that the base is a square where the length, l, and the width, w. are equal.
Anyway, back to the given problem!
a) Solve for w:
{{{V = (1/3)l*w*h}}} Multiply both sides by 3.
{{{3V = l*w*h}}} Now divide both sides by {{{l*h}}}
{{{3V/(l*h) = w}}} or {{{highlight(w = 3V/(l*h))}}}
b) A "square" pyramid has a volumre of 560 sq.in, a base length of 10 in., and a height of 14 in. FInd the width of the base.
(If it were truly a "square" pyramid, the width would be 10 in.)
Let's apply the formula we just derived for w:
{{{w = 3V/(l*h)}}} Substitute V = 560, l = 10, and h = 14.
{{{w = 3(560)/(10*14)}}} Evaluate.
{{{w = 1680/140}}}
{{{w = 12}}}in.