MATH SOLVE

6 months ago

Q:
# 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]

[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]