Calculating the Volume of a Solid Oblique Pyramid

Oct 13, 2025 by talynt.org 133 views

**A Solid Oblique Pyramid: Understanding the Volume Calculation**

What is a Solid Oblique Pyramid?

A solid oblique pyramid is a three-dimensional geometric shape that has a square base and four triangular faces that meet at the apex. Unlike a right pyramid, an oblique pyramid does not have its apex directly above the center of the base, resulting in a more complex shape.

Calculating the Volume of a Solid Oblique Pyramid

To calculate the volume of a solid oblique pyramid, we need to know the area of the base and the height of the pyramid. The formula for the volume of a pyramid is:

V = (1/3) * B * h

where V is the volume, B is the area of the base, and h is the height of the pyramid.

Given Information

In this problem, we are given a solid oblique pyramid with a square base with an edge length of 2 cm. Angle BAC measures $$45^{\circ}$$ and AC measures 3.6 cm.

Step 1: Find the Height of the Pyramid

To find the height of the pyramid, we can use the given angle and the length of AC. Since angle BAC measures $$45^{\circ}$$, we can draw a right triangle with AC as the hypotenuse and the height of the pyramid as one of the legs.

Using the trigonometric function, we can find the height of the pyramid:

h = AC * sin(45°)

h = 3.6 * sin(45°)

h = 3.6 * 0.7071

h ≈ 2.55 cm

Step 2: Find the Area of the Base

The area of the base is the square of the edge length:

B = edge^2

B = 2^2

B = 4 cm^2

Step 3: Calculate the Volume of the Pyramid

Now that we have the area of the base and the height of the pyramid, we can calculate the volume:

V = (1/3) * B * h

V = (1/3) * 4 * 2.55

V ≈ 3.4 cm^3

Conclusion

The volume of the solid oblique pyramid is approximately 3.4 cm^3.

Q&A

Q: What is the formula for the volume of a pyramid?

A: The formula for the volume of a pyramid is V = (1/3) * B * h, where V is the volume, B is the area of the base, and h is the height of the pyramid.

Q: How do I find the height of the pyramid?

A: To find the height of the pyramid, you can use the given angle and the length of AC. Draw a right triangle with AC as the hypotenuse and the height of the pyramid as one of the legs. Then, use the trigonometric function to find the height.

Q: What is the area of the base of the pyramid?

A: The area of the base is the square of the edge length. In this problem, the edge length is 2 cm, so the area of the base is 4 cm^2.

Q: How do I calculate the volume of the pyramid?

A: To calculate the volume of the pyramid, you need to multiply the area of the base by the height of the pyramid and then divide by 3.

Q: What is the volume of the solid oblique pyramid?

A: The volume of the solid oblique pyramid is approximately 3.4 cm^3.

Common Mistakes

Forgetting to multiply the area of the base by the height of the pyramid
Not using the correct formula for the volume of a pyramid
Not drawing a right triangle to find the height of the pyramid

Tips and Tricks

Make sure to use the correct formula for the volume of a pyramid
Draw a right triangle to find the height of the pyramid
Check your calculations to ensure that you are getting the correct answer