Respuesta :
The volume of a pyramid can be calculated with this formula:
[tex]V=\frac{Bh}{3}[/tex]Where "B" is the area of the base and "h" is the height of the pyramid.
The area of a triangle can be found using this formula:
[tex]A=\frac{bH}{2}[/tex]Where "b" is the base of the triangle and "H" is the height.
In this case you know that:
[tex]\begin{gathered} b=9in \\ H=4in \end{gathered}[/tex]Then:
[tex]B=\frac{(9in)(4in)}{2}=18in^2[/tex]Knowing "V" and "B", you can substitute values into the formula:
[tex]\begin{gathered} V=\frac{Bh}{3} \\ \\ (48in^3)=\frac{(18in^2)h}{3} \end{gathered}[/tex]Finally, you must solve for "h":
[tex]\begin{gathered} (48in^3)=\frac{(18in^2)h}{3} \\ \\ (3)(48in^3)=(18in^2)h \\ 144in^3=(18in^2)h \\ \\ \frac{144in^3}{18in^2}=h \\ \\ h=8in \end{gathered}[/tex]The answer is:
[tex]8in[/tex]