Find the volume of the figure when b = 3 ft and h = 6 ft. ________________ ft3 ### Understanding the Regular Tetrahedron**Figure Description:**The image depicts a geometric figure known as a regular tetrahedron. A tetrahedron is a type of polyhedron that consists of four triangular faces, with three meeting at each vertex.**Labels:**- **b**: This represents the length of the base edge of the tetrahedron.- **h**: This denotes the height of the tetrahedron, which is the perpendicular distance from the base to the apex (the top vertex opposite the base).### Detailed Explanation:1. **Base Edges (b):** - All edges of a regular tetrahedron are equal in length. Here, each edge is labeled with $ b $, indicating that the lengths are uniform.2. **Height of the Tetrahedron (h):** - The height $ h $ is the perpendicular distance from a vertex (the apex) of the tetrahedron to the center of the base. 3. **3D Representation:** - Dashed lines are used to depict edges that are not directly visible in a solid three-dimensional view, helping in visualizing the internal structure.### Educational Insight:A regular tetrahedron is one of the simplest forms of polyhedra and has significant importance in fields such as chemistry, where it represents the structure of molecules like methane (CH₄). Understanding its properties, such as edge length and height, is fundamental in grasping more complex geometric and spatial concepts.

The given figure is a right square pyramid.

Answered: Find the volume of the figure when b…

Math

Algebra

Find the volume of the figure when b = 3 ft and h = 6 ft. ________________ ft3

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.

Question

Find the volume of the figure when

b = 3 ft and h = 6 ft.

________________ ft³

### Understanding the Regular Tetrahedron

**Figure Description:**
The image depicts a geometric figure known as a regular tetrahedron. A tetrahedron is a type of polyhedron that consists of four triangular faces, with three meeting at each vertex.

**Labels:**
- **b**: This represents the length of the base edge of the tetrahedron.
- **h**: This denotes the height of the tetrahedron, which is the perpendicular distance from the base to the apex (the top vertex opposite the base).

### Detailed Explanation:

1. **Base Edges (b):**
- All edges of a regular tetrahedron are equal in length. Here, each edge is labeled with $ b $, indicating that the lengths are uniform.

2. **Height of the Tetrahedron (h):**
- The height $ h $ is the perpendicular distance from a vertex (the apex) of the tetrahedron to the center of the base.

3. **3D Representation:**
- Dashed lines are used to depict edges that are not directly visible in a solid three-dimensional view, helping in visualizing the internal structure.

### Educational Insight:
A regular tetrahedron is one of the simplest forms of polyhedra and has significant importance in fields such as chemistry, where it represents the structure of molecules like methane (CH₄). Understanding its properties, such as edge length and height, is fundamental in grasping more complex geometric and spatial concepts.

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