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 10 square inches and a height of 9 inches?
The volume of the pyramid is cubic inches.
The solution is

Step 1 ：The volume of a pyramid is given by the formula \(V = \frac{1}{3} * B * h\), where \(B\) is the base area and \(h\) is the height.

Step 2 ：We know that the volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. We can use this information to find the constant of variation, \(k\), in the formula \(V = k * B * h\).

Step 3 ：Substituting the given values into the formula, we get \(24 = k * 24 * 3\). Solving for \(k\), we find that \(k = 0.3333333333333333\).

Step 4 ：We can now use the value of \(k\) to find the volume of a pyramid with a base area of 10 square inches and a height of 9 inches.

Step 5 ：Substituting the values of \(B = 10\) and \(h = 9\) into the formula \(V = k * B * h\), we get \(V = 0.3333333333333333 * 10 * 9\), which simplifies to \(V = 29.999999999999996\).

Step 6 ：Rounding to the nearest whole number, we find that the volume of the pyramid with a base area of 10 square inches and a height of 9 inches is approximately \(\boxed{30}\) cubic inches.