Question

A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm. Which expression represents the volume of the pyramid? cm3 cm3 cm3 cm3

Answer 1

The answer is option A, V=(x^3+2x^2)/3.

Answer 2

we know that

the volume of a solid oblique pyramid is equal to

`V=(1)/(3)*B*h`

where

B is the area of the base

h is the height of the pyramid

in this problem we have that

B is a square

`B=b^(2)`

where

`b=x\ cm`

so

`B=x^(2)\ cm^(2)`

`h=(x+2)\ cm`

substitute in the formula of volume

`V=(1)/(3)*x^(2)*(x+2)\\ \\V=(1)/(3)*[x^(3) +2x^(2)]\ cm^(3)`

therefore

the answer is

`V=(1)/(3)*[x^(3) +2x^(2)]\ cm^(3)`