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.
v = k A h
24 = k 24 * 3
so
k = 1/3 (this is not news by the way:)
v = (1/3)(15)(7)
= 35 cubic inches
By the way:
The volume of any shape with pointy top and straight sides is (1/3)(base area)(height)
---->cone, pyramid, whatever
Well, let's do some math and find out!
Since the volume of the pyramid varies jointly with the base area and the height, we can set up a proportion:
(24 cubic inches) / (24 square inches * 3 inches) = (x cubic inches) / (15 square inches * 7 inches)
Now, let's cross multiply and solve for x:
(24 cubic inches) * (15 square inches * 7 inches) = (24 square inches * 3 inches) * (x cubic inches)
Let me do some quick calculations...
24 * 15 * 7 = 2520
24 * 3 = 72
So, we have:
2520 = 72x
Dividing both sides by 72, we get:
x = 2520 / 72
That simplifies to:
x = 35
So, the volume of the pyramid with a base area of 15 square inches and a height of 7 inches is 35 cubic inches.
Hope that answers your question!
To solve this problem, we can use the given information to set up a proportion and solve for the volume of the second pyramid.
Let's use the variables V1, A1, and h1 to represent the volume, base area, and height of the first pyramid, and V2, A2, and h2 for the second pyramid.
According to the problem, the volume of the first pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. This can be written as:
V1 = 24 cubic inches
A1 = 24 square inches
h1 = 3 inches
We can establish a proportion with these values:
V1 / A1 * h1 = V2 / A2 * h2
Plugging in the values we know:
24 / 24 * 3 = V2 / 15 * 7
Simplifying the equation:
1 * 3 = V2 / (15 * 7)
3 = V2 / 105
To find V2, we can cross-multiply:
V2 = 3 * 105
V2 = 315
Therefore, the volume of the pyramid with a base area of 15 square inches and a height of 7 inches is 315 cubic inches.
To find the volume of a pyramid, you need to know the formula for its volume and the given values of its base area and height.
The formula for the volume of a pyramid is given by V = (1/3) * base area * height.
In this problem, you are given that the volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.
Let's use this given information to find the constant of variation that relates the volume, base area, and height of the pyramid.
Since the volume varies jointly with the base area and height, we can write the equation as:
V = k * A * H,
where V is the volume, A is the base area, H is the height, and k is the constant of variation.
Using the given values, we can substitute them into the equation and solve for k:
24 = k * 24 * 3.
Dividing both sides of the equation by (24 * 3), we get:
24 / (24 * 3) = k.
Simplifying the expression, we have:
1 / 3 = k.
Now that we have the value of k, we can use it to find the volume of a pyramid with a base area of 15 square inches and a height of 7 inches.
Substituting the values into the equation, we get:
V = (1/3) * 15 * 7.
Evaluating the expression, we have:
V = (1/3) * 105.
Simplifying the expression, we get:
V = 35.
Therefore, the volume of the pyramid with a base area of 15 square inches and a height of 7 inches is 35 cubic inches.