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

The formula for the volume of a square pyramid in terms of h is
`h=(3V)/(s^2)`

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

Explanation:

We are given the formula for the volume of a square pyramid as
`V=(1)/(3)s^2h`

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

`\mathrm{Switch\:sides}\\(1)/(3)s^2h=V`

`\mathrm{Divide\:both\:sides\:by\:}(1)/(3)s^2\\((1)/(3)s^2h)/((1)/(3)s^2)=(V)/((1)/(3)s^2)`

`\mathrm{Simplify}\\((1)/(3)s^2h)/((1)/(3)s^2) = h`

`\mathrm{Simplify\:}\\(V)/((1)/(3)s^2)= (3V)/(s^2)`

So

`h=(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=(3V)/(s^2)\\\\h=(3\cdot 400)/(10^2)\\h=12 \:cm`