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

$V=\frac{1}{3}*B*h$

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

$V=\frac{1}{3}*x^{2}*(x+2)\\ \\V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}$

therefore

the answer is

$V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}$