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Math Formula Cube and Cuboid

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Math Formula Cube and Cuboid - Formula Quest

Math Formulas for Cubes and Cuboids

Cube

A cube is a three-dimensional shape with six equal square faces. All sides of a cube have the same length.

Formulas:

  • Volume of a Cube (V):
V = a^3

where a is the length of a side of the cube.

  • Surface Area of a Cube (SA):
SA = 6a^2

where a is the length of a side of the cube.

Example:

If the side length a of a cube is 4 cm:

  • Volume:
V = 4^3 = 64 cm^3
  • Surface Area:
SA = 6 × 4^2 = 6 × 16 = 96 cm^2

Cuboid

A cuboid is a three-dimensional shape with six rectangular faces. The faces can be of different lengths.

Formulas:

  • Volume of a Cuboid (V):
V = l × w × h

where l is the length, w is the width, and h is the height.

  • Surface Area of a Cuboid (SA):
SA = 2(lw + lh + wh)

where l is the length, w is the width, and h is the height.

Example:

If a cuboid has a length l of 5 cm, a width w of 3 cm, and a height h of 4 cm:

  • Volume:
V = 5 × 3 × 4 = 60 cm^3
  • Surface Area:
SA = 2(5 × 3 + 5 × 4 + 3 × 4) = 2(15 + 20 + 12) = 2 × 47 = 94 cm^2

Summary

  • The volume of a cube is found by cubing the length of one side.
  • The surface area of a cube is six times the area of one of its faces.
  • The volume of a cuboid is found by multiplying its length, width, and height.
  • The surface area of a cuboid is found by summing the areas of all its rectangular faces and then doubling the result.

These formulas are essential for calculating the properties of cubes and cuboids in various mathematical and real-world applications.

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