Question

The square pyramid has a volume of 288 cubic inches. What is the value of x? Please respond ASAP

Answer 1

`x=12in`

Explanation:

the formula for the volume of a square pyramid is:

`V=(Ab*h)/(3)`

where

`Ab` is the area of the base (the area of the square)

and
`h` if the height of the pyramid

---------

the length of the side of the square is
`x`, so the area of the base of the pyramid is:

`Ab=x*x=x^2`

and we already know the height in terms of x:

`h=(1)/(2)x`

and the Volume:

`V=288in^3`

so we subtitute all of this in the formula for volume:

`288=(x^2((1)/(2)x ))/(3) \\288=(x^3)/(6)`

and finally we clear for
`x`

`288*6=x^3\\1728=x^3\\\sqrt[3]{1728}=x\\12=x`

the value of x is 12 inches.

Answer 2

x = 12 in

Explanation:

The diagram depicts a Right-Pyramid with a square base. The height of the pyramid is given as
`(x)/(2)\text{ in}` and the side of the base is given as
`x\text{ in}`.

For any pyramid, the volume is given by the result

`\text{Volume = }(1)/(3)* \text{ Area of base }* \text{ Height}`

So, Volume of given pyramid =
`(1)/(3)* (x^(2)\text{ in}^(2)) *((x)/(2) \text{ in})=(x^(3))/(6)\text{ in}^(3)`

Volume is given as
`288\text{ in}^(3)`

`(x^(3))/(6)\text{ = }288\text{ in}^(3)\\\\x^(3)\text{ = }1728\text{ in}^(3)\\x\text{ = }12\text{ in}`

∴ Value of
`x` =
`12\text{ in}`