ANSWER
[tex] x= 9 \: in[/tex]
EXPLANATION
The volume of a rectangular prism is given by the formula,
[tex]V = l \times b \times h[/tex]
We substitute the dimensions to obtain,
[tex]V = 6 \times 3 \times 12 \: {in}^{3} [/tex]
The volume of the rectangular pyramid is,
[tex]V = \frac{1}{3} \times 6 \times 12 \times x \: {in}^{3} [/tex]
Equating the two volumes gives,
[tex]\frac{1}{3} \times 6 \times 12 \times x = 6 \times 3 \times 12[/tex]
We divide through by 6×12 to get,
[tex] \frac{x}{3}=3[/tex]
We solve for x to obtain,
[tex]x = 3 \times 3[/tex]
[tex]x = 9 \: in[/tex]
