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?
30
V=24*10/24*9/3
To find the volume of a pyramid with a base area of 10 square inches and a height of 9 inches, we can use the given information about the variation.
First, let's write the variation equation:
Volume = k * Base Area * Height
To find the value of k, we can use the given information about one pyramid:
Volume = 24 cubic inches
Base Area = 24 square inches
Height = 3 inches
Plugging these values into the equation, we have:
24 = k * 24 * 3
Now, we can solve for k:
k = 24 / (24 * 3)
Simplifying this, we get:
k = 1 / 3
Now, we can use this value of k to find the volume of the pyramid with a base area of 10 square inches and a height of 9 inches:
Volume = (1/3) * Base Area * Height
Volume = (1/3) * 10 * 9
Volume = (1/3) * 90
Volume = 30 cubic inches
Therefore, the volume of the pyramid with a base area of 10 square inches and a height of 9 inches is 30 cubic inches.
To find the volume of a pyramid, you need to use the proportional equation that relates the volume of the pyramid, the base area, and the height. In this case, we know that the volume is directly proportional to the base area and the height.
Let's represent the volume as V, the base area as A, and the height as H. Then the formula becomes:
V = k × A × H,
where k is the constant of variation.
Now we can use the given information to solve for k. We are given that when A = 24 square inches and H = 3 inches, V = 24 cubic inches. Plugging in these values to the equation, we have:
24 = k × 24 × 3.
Simplifying this equation, we get:
1 = k × 3.
Dividing both sides by 3, we find:
k = 1/3.
Now that we have the constant of variation, we can determine the volume of a pyramid with the given base area and height. Let's use A = 10 square inches and H = 9 inches:
V = (1/3) × 10 × 9.
Calculating this expression, we find:
V = 30 cubic inches.
Therefore, the volume of the pyramid with a base area of 10 square inches and a height of 9 inches is 30 cubic inches.