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.
v = k * Ab * h
24 = k * 24 * 3 ... 1/3 = k
v = 1/3 * 10 * 9
To solve this problem, we can use the proportionality relationship stated in the question. Let's call the volume V, the base area A, and the height H.
According to the given information, we know that the volume (V) varies jointly with the base area (A) and the height (H), which can be written as:
V = k * A * H
where k is the constant of proportionality.
We are given the information that when A = 24 square inches and H = 3 inches, V = 24 cubic inches. We can use this information to find the value of k.
Using the given values, we have:
24 = k * 24 * 3
Simplifying the equation, we get:
1 = k * 3
Now, solving for k, we find:
k = 1/3
Now, we can use the value of k to find the volume (V) when A = 10 square inches and H = 9 inches.
Substituting the values into the formula, we have:
V = (1/3) * 10 * 9
Simplifying, we get:
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.
To find the volume of a pyramid with a base area of 10 square inches and a height of 9 inches, you can use the given information about the variation between the volume, base area, and height.
We are told that the volume of a pyramid varies jointly with the base area and height, which means we can write an equation to express this relationship mathematically:
Volume = k * Base Area * Height,
where k is a constant.
We are then given specific values for the volume, base area, and height of one pyramid:
Volume = 24 cubic inches,
Base Area = 24 square inches, and
Height = 3 inches.
Using these values, we can substitute them into the equation to solve for k:
24 = k * 24 * 3.
Dividing both sides of the equation by (24 * 3), we get:
k = 24 / (24 * 3) = 1/3.
Now that we have determined the value of k, we can use it to find the volume of a pyramid with a base area of 10 square inches and a height of 9 inches:
Volume = (1/3) * Base Area * Height.
Plugging in the values, we get:
Volume = (1/3) * 10 * 9 = 3 * 10 = 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.