Question

The formula for the volume of a square pyramidis

v=6h) - 3, where b is the length of one side of the
square base and h is the height of the pyramid. Find the
length of a side of the base of a square pyramid that has
a height of 3 inches and a volume of 25 cubic inches.
Show your work.

Answer 1

5 inches

Explanation:

The volume is basically

Volume = area of base * height

For pyramid, that area would be
`(1)/(3)`

Since, this is square pyramid, the base is a square with side length b, so the area would be
`b^2`

Let height be h

Thus, we can write the formula for volume of square pyramid as:

Volume =
`(1)/(3)b^2h`

Where

b is side length of base square

h is height of pyramid

Now, given h = 3 and v = 25, we need to find b. let's substitute and figure it out using the formula:

`V=(1)/(3)b^2 h\\25=(1)/(3)b^2 (3)\\25=b^2\\b=√(25)\\b=5`

Hence

the side length of the base of the square pyramid is 5 inches