Question

the volume of a pyramid varies jointly with the base area of the pyramid and its height. the volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. what is the volume of a pyramid with a base area of 15 square inches and a height of 7 inches? the volume of the pyramid is cubic inches. the solution is

Explanation:

Step1: Find the constant of variation

Since $V$ (volume) varies jointly with $B$ (base - area) and $h$ (height), the formula is $V = kBh$. We know that $V = 24$ cubic inches, $B = 24$ square inches, and $h = 3$ inches. Substitute these values into the formula: $24=k\times24\times3$. Solve for $k$:
\[

$$\begin{align*} 24&=k\times72\\ k&=\frac{24}{72}\\ k&=\frac{1}{3} \end{align*}$$

\]

Step2: Calculate the new volume

Now that we have $k=\frac{1}{3}$, and we are given $B = 15$ square inches and $h = 7$ inches. Substitute these values into the formula $V = kBh$:
\[

$$\begin{align*} V&=\frac{1}{3}\times15\times7\\ V& = 5\times7\\ V&=35 \end{align*}$$

\]

Answer:

35