Question

The volume of a pyramid very jointly as its height and the area of its base the pyramid has a height of 15 feet and base area of 10 feet squared and a volume of 50 feet cubed what is the height of a pyramid that has a volume of 60 feet cubed and a base area of 12 feet squar

Answer 1

`\bf \begin{array}{cccccclllll} \textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\ \textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\ y&=&{{ k}}&\cdot&x \\ && y={{ k }}x \end{array}`

"The volume of a pyramid very jointly as its height and the area of its base the pyramid "
`\bf V=kBh\qquad \begin{cases} k=\textit{constant of variation}\\ B=\textit{area of base}\\ h=height \end{cases} \\\\\\ \textit{now, we know that } \begin{cases} h=15\\ B=10\\ V=50 \end{cases}\implies 50=k\cdot 10\cdot 15 \\\\\\ 50=150k\implies \cfrac{50}{150}=k\implies \cfrac{1}{3}=k \\\\\\ thus\implies \boxed{V=\cfrac{1}{3}Bh}`

now, what's the height of a pyramid with V=60 and B=12?
`\bf \begin{array}{llll} 60=\cfrac{1}{3}\cdot &10\cdot h\\ \uparrow &\uparrow \\ V&B \end{array}`

solve for "h"