The oblique pyramid has a square base with an edge length of 5 cm. The height of the pyramid is 7 cm.
Answer (2)
Calculate the area of the square base: A = 5 2 = 25 cm 2 .
Apply the pyramid volume formula: V = 3 1 ∗ A ∗ h .
Substitute the values: V = 3 1 ∗ 25 ∗ 7 = 3 175 cm 3 .
The volume of the pyramid is: 58 3 1 cm 3 .
Explanation
Problem Analysis We are given an oblique pyramid with a square base. The edge length of the square base is 5 cm, and the height of the pyramid is 7 cm. Our goal is to find the volume of this pyramid.
Volume Formula The volume of a pyramid is given by the formula: V = 3 1 ∗ A ∗ h where V is the volume, A is the area of the base, and h is the height of the pyramid. In our case, the base is a square with an edge length of 5 cm, and the height is 7 cm.
Calculate Base Area First, we need to calculate the area of the square base. The area of a square is given by the formula: A = s 2 where s is the side length of the square. In our case, s = 5 cm, so the area of the base is: A = 5 2 = 25 cm 2
Calculate Volume Now that we have the area of the base, we can calculate the volume of the pyramid. Using the volume formula: V = 3 1 ∗ A ∗ h = 3 1 ∗ 25 ∗ 7 = 3 175 = 58 3 1 cm 3
Final Answer Therefore, the volume of the oblique pyramid is 58 3 1 cm 3 .
Examples
Understanding the volume of pyramids is useful in architecture and construction. For example, when designing a pyramid-shaped structure, knowing how to calculate the volume helps determine the amount of material needed, which directly impacts cost and structural integrity. This ensures efficient use of resources and a stable, safe design.
The volume of the oblique pyramid is calculated using the formula V = 3 1 A h . With a square base area of 25 cm² and height of 7 cm, the final volume is 58 3 1 cm 3 .
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