Question

The volume v of a pyramid with a square base with side length s and height h is upper v equals one third s squared hv= 1 3s2h. solved forâ s, this formula gives s equals startroot startfraction 3 upper v over h endfraction endroots= 3v h. a pyramid has a volume of approximately 7 comma 700 comma 0007,700,000 cubic meters. find the length of the side of the pyramid if its height is approximately 148148 meters.

Answer 1

In this question,it is given that,

The volume v of a pyramid with a square base with side length s and height h is

$V = \frac{1}{3} s^2 h$

And we have to solve for s.

First we will get rid of 3 by multiplying both sides by 3, that is

$3V = s^2h \\ s^2 = \frac{3V}{h} \\ s = \sqrt{ \frac{3V}{h}}$

And in the next part it is given that , volume is 7700 cubic meters and height is 148 meters .

Substituting these values, we will get

$s = \sqrt{ \frac{3V}{h}} \\ s = \sqrt{ \frac{3*7700}{148}} = 12.5 meters$