A rectangular pyramid has a base with dimensions 5 inches by 7 inches. The height of the pyramid is unknown. If the volume of the pyramid is 105 cubic inches, what is the height of the pyramid? Explain the steps
Accepted Solution
A:
bearing in mind that the volume of a pyramid is the product of the area of its base and its height, now, this one has a rectangular base of 5x7, so its base area is 35. [tex] \bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ ------\\ V=\stackrel{in^3}{105}\\ B=\stackrel{5\times 7}{35} \end{cases}\implies 105=\cfrac{1}{3}(35)h \\\\\\ 3(105)=35h\implies 315=35h\implies \cfrac{315}{35}=h\implies 9=h [/tex]