Question

The volume of the triangular pyramid below is 99 units^3. Find the value of x.

Answer 1

11

Explanation:

The formula for a triangular pyramid is:

V = 1/3 × base area × height

(base area is base × height ÷ 2 so x × 6 ÷ 2)

99 = 1/3 × 6x/2 × 9 divide equation by 9

÷9 ÷9

3(11 = 1/3 × 6x/2) multiple equation by 3

(33 = 6x/2) multiple by 2

66 = 6x divide by 6

÷6 ÷6

11 = x

Answer 2

Check the picture below.

so the pyramid has a base area of "B" and a height of "h", thus

`\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=(1)/(2)(x)(6)\\[1em] h=9\\ V=99 \end{cases}\implies 99=\cfrac{1}{3}\stackrel{B}{\left[\cfrac{1}{2}(x)(6) \right]}(\stackrel{h}{9}) \\\\\\ 99=\cfrac{1}{3}(3x)(9)\implies 99=9x\implies \cfrac{99}{9}=x\implies 11=x`