a solid oblique pyramid has a square base with edges measuring x cm. the height of the pyramid is (x + 2)…

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? \\(\\frac{x^3 + 2x^2}{3}\\) cm³ \\(\\frac{x^2 + 2x^2}{2}\\) cm³ \\(\\frac{x^3}{3}\\) cm³ \\(\\frac{x^3 + 2x^2}{2}\\) cm³

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? \\(\\frac{x^3 + 2x^2}{3}\\) cm³ \\(\\frac{x^2 + 2x^2}{2}\\) cm³ \\(\\frac{x^3}{3}\\) cm³ \\(\\frac{x^3 + 2x^2}{2}\\) cm³

Answer

Explanation:

Step1: Recall the volume formula for a pyramid

The volume ( V ) of a pyramid is given by ( V=\frac{1}{3}Bh ), where ( B ) is the area of the base and ( h ) is the height.

Step2: Calculate the area of the square base

The base is a square with edge length ( x ) cm. The area of a square is ( B = \text{side}^2 ), so ( B=x^2 ) ( \text{cm}^2 ).

Step3: Substitute ( B ) and ( h ) into the volume formula

The height ( h=(x + 2) ) cm. Substituting ( B = x^2 ) and ( h=(x + 2) ) into ( V=\frac{1}{3}Bh ), we get: [ V=\frac{1}{3}\times x^2\times(x + 2) ]

Step4: Expand the expression

Using the distributive property ( a(b + c)=ab+ac ), where ( a = x^2 ), ( b=x ), and ( c = 2 ), we have ( x^2\times(x + 2)=x^3+2x^2 ). So the volume is: [ V=\frac{x^3 + 2x^2}{3}\text{ cm}^3 ]

Answer: (\frac{x^{3}+2x^{2}}{3}\text{ cm}^3) (the first option)