Respuesta :
Answer:
The formula for the volume of a square pyramid in terms of h is [tex]h=\frac{3V}{s^2}[/tex]
The height of a square pyramid with V = 400 [tex]cm^3[/tex] and s = 10 cm is 12 cm
Step-by-step explanation:
We are given the formula for the volume of a square pyramid as [tex]V=\frac{1}{3}s^2h[/tex]
- To rewrite the formula in terms of h you need to:
[tex]\mathrm{Switch\:sides}\\\frac{1}{3}s^2h=V[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}\frac{1}{3}s^2\\\frac{\frac{1}{3}s^2h}{\frac{1}{3}s^2}=\frac{V}{\frac{1}{3}s^2}[/tex]
[tex]\mathrm{Simplify}\\\frac{\frac{1}{3}s^2h}{\frac{1}{3}s^2} = h[/tex]
[tex]\mathrm{Simplify\:}\\\frac{V}{\frac{1}{3}s^2}= \frac{3V}{s^2}[/tex]
So
[tex]h=\frac{3V}{s^2}[/tex]
- To find the height of a square pyramid with volume V = 400 [tex]cm^3[/tex] and side lengths s = 10 cm you need to replace these values into the following formula:
[tex]h=\frac{3V}{s^2}\\\\h=\frac{3\cdot 400}{10^2}\\h=12 \:cm[/tex]
