The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 12 feet and a base with area of 23 square feet has a volume of 92 cubic feet. Find the volume of a pyramid with a height of 17 and a base with an area of 27 square feet.
v = kha
92 = k(12)(23)
92 = 276k
k = 92/276 = 1/3
v = 1/3ha
v = (1/3)(17)(27)
v = 153
The base of a triangular pyramid has an area of 20 square feet . The height of the pyramid is 36 feet . The volume of the pyramid is Response area cubic feet.
The base of a triangular pyramid has an area of 20 square feet . The height of the pyramid is 36 feet . The volume of the pyramid is
Thank you
To solve this problem, we can set up a proportion to find the volume of the pyramid with a height of 17 and a base with an area of 27 square feet.
First, let's assign variables to the given values:
- Let's call the volume of the first pyramid V1, the height h1, and the base area B1.
- Similarly, let's call the volume of the second pyramid V2, the height h2, and the base area B2.
From the given information, we know that:
V1 = 92 cubic feet,
h1 = 12 feet,
B1 = 23 square feet.
According to the problem statement, the volume of the pyramid varies jointly as its height and the area of its base. This can be represented by the equation:
V = k * h * B,
where V is the volume, h is the height, B is the base area, and k is a constant of proportionality.
Applying this equation to both pyramids, we can write the following proportions:
V1 = k * h1 * B1,
V2 = k * h2 * B2.
To find the value of k, we can use the first pyramid's given values:
92 = k * 12 * 23.
Now, solve for k:
k = 92 / (12 * 23).
k ≈ 0.3333 cubic feet per square foot per foot.
Now, we can use this value of k to find the volume of the second pyramid:
V2 = k * h2 * B2,
V2 = 0.3333 * 17 * 27.
Calculating this expression:
V2 ≈ 153.9991 cubic feet.
Therefore, the volume of the pyramid with a height of 17 feet and a base area of 27 square feet is approximately 154 cubic feet.