Question

the formula for the volume of a square pyramid is V=1/3s2h. rewrite the formula in terms of h. then find the height of a square pyramid with volume V=400cm3 and side lengths s=10cm

Answer 1

Answer:

The formula for the volume of a square pyramid in terms of h is $h=\frac{3V}{s^2}$

The height of a square pyramid with V = 400 $cm^3$ and s = 10 cm is 12 cm

Step-by-step explanation:

We are given the formula for the volume of a square pyramid as $V=\frac{1}{3}s^2h$

• To rewrite the formula in terms of h you need to:

$\mathrm{Switch\:sides}\\\frac{1}{3}s^2h=V$

$\mathrm{Divide\:both\:sides\:by\:}\frac{1}{3}s^2\\\frac{\frac{1}{3}s^2h}{\frac{1}{3}s^2}=\frac{V}{\frac{1}{3}s^2}$

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

$\mathrm{Simplify\:}\\\frac{V}{\frac{1}{3}s^2}= \frac{3V}{s^2}$

So

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

• To find the height of a square pyramid with volume V = 400 $cm^3$ and side lengths s = 10 cm you need to replace these values into the following formula:

$h=\frac{3V}{s^2}\\\\h=\frac{3\cdot 400}{10^2}\\h=12 \:cm$