Regular Hexagonal Base Area

Oct 13, 2025 by wbrum.org 134 views

**A Solid Right Pyramid: Understanding the Volume of a Regular Hexagonal Base**

What is a Solid Right Pyramid?

A solid right pyramid is a three-dimensional geometric shape that consists of a regular polygon as its base and a set of triangular faces that meet at the apex. The base of the pyramid is a regular hexagon, which means that all its sides are equal in length and all its internal angles are equal.

Understanding the Volume of a Pyramid

The volume of a pyramid is given by the formula:

V = (1/3) * B * h

Where:

V is the volume of the pyramid
B is the area of the base of the pyramid
h is the height of the pyramid

Calculating the Volume of a Pyramid with a Regular Hexagonal Base

Given that the area of the regular hexagonal base is 5.2 cm^2 and the height of the pyramid is h cm, we can use the formula to calculate the volume of the pyramid.

Q: What is the expression that represents the volume of the pyramid?

A: The expression that represents the volume of the pyramid is:

V = (1/3) * 5.2 * h

Q: How do I simplify the expression to find the volume of the pyramid?

A: To simplify the expression, we can multiply the numbers together:

V = (1/3) * 5.2 * h V = 1.7333 * h

Q: What is the final expression that represents the volume of the pyramid?

A: The final expression that represents the volume of the pyramid is:

V = (1/3) * 5.2 * h V = 1.7333 * h

However, since the answer choices are given in a specific format, we can rewrite the expression as:

V = (1/3) * 5.2h

Q: Why is the expression (1/3) * 5.2h the correct answer?

A: The expression (1/3) * 5.2h is the correct answer because it represents the volume of the pyramid using the given area of the base (5.2 cm^2) and the height of the pyramid (h cm).

Conclusion

In conclusion, the expression that represents the volume of the pyramid is (1/3) * 5.2h. This expression uses the given area of the base (5.2 cm^2) and the height of the pyramid (h cm) to calculate the volume of the pyramid.

Frequently Asked Questions

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.
Q: What is the area of the base of the pyramid? A: The area of the base of the pyramid is 5.2 cm^2.
Q: What is the height of the pyramid? A: The height of the pyramid is h cm.
Q: How do I calculate the volume of the pyramid? A: To calculate the volume of the pyramid, use the formula V = (1/3) * B * h, where B is the area of the base and h is the height of the pyramid.

Additional Resources

Pyramid Volume Formula: V = (1/3) * B * h
Regular Hexagonal Base Area: 5.2 cm^2
Pyramid Height: h cm

References

Geometry Textbook: Chapter 5, Section 3
Mathematics Online Resource: Pyramid Volume Formula