3d Geometric Shapes Formulas

4 min read Jul 07, 2024
3d Geometric Shapes Formulas

3D Geometric Shapes Formulas

In mathematics, 3D geometric shapes are an essential concept in understanding spatial relationships and calculations. These shapes have various formulas to calculate their surface area, volume, and other properties. In this article, we will discuss some of the most common 3D geometric shapes and their formulas.

1. Rectangular Prism

A rectangular prism is a 3D shape with six rectangular faces.

Formulas:

  • Volume (V): V = lwh, where l is the length, w is the width, and h is the height.
  • Surface Area (SA): SA = 2(lw + lh + wh)

2. Cube

A cube is a special type of rectangular prism with all sides of equal length.

Formulas:

  • Volume (V): V = s^3, where s is the side length.
  • Surface Area (SA): SA = 6s^2

3. Pyramid

A pyramid is a 3D shape with a polygonal base and triangular faces that meet at the apex.

Formulas:

  • Volume (V): V = (1/3)Bh, where B is the base area and h is the height.
  • Surface Area (SA): SA = B + (1/2)Pl, where P is the perimeter of the base and l is the slant height.

4. Cylinder

A cylinder is a 3D shape with two parallel and circular bases connected by a curved lateral surface.

Formulas:

  • Volume (V): V = πr^2h, where r is the radius and h is the height.
  • Surface Area (SA): SA = 2πr(r + h)

5. Cone

A cone is a 3D shape with a circular base and a curved lateral surface that tapers to a point.

Formulas:

  • Volume (V): V = (1/3)πr^2h, where r is the radius and h is the height.
  • Surface Area (SA): SA = πr(r + l), where l is the slant height.

6. Sphere

A sphere is a 3D shape that is symmetrical about its center.

Formulas:

  • Volume (V): V = (4/3)πr^3, where r is the radius.
  • Surface Area (SA): SA = 4πr^2

These formulas are essential in various mathematical and real-world applications, such as architecture, engineering, and physics. Mastery of these formulas will help you solve complex problems and understand the properties of 3D geometric shapes.

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