"Volume of a pyramid"

Volume of a Pyramid

• Definition of a Pyramid:

  • A pyramid is a three-dimensional geometric shape with a polygonal base and triangular faces that meet at a single point (the apex).

• Volume Formula for a Pyramid:

  • The volume () of a pyramid can be calculated using the formula:
    $V = \frac{1}{3} Bh$
    Where:
  • $B$ = Area of the base
  • $h$ = Height of the pyramid

• Calculating the Base Area:

  • If the base of the pyramid is a rectangle:
  • The area of the rectangle is calculated as:
    $B = \text{length} \times \text{width}$
  • For the given sample, the length and width both are 7 ft.
    • Calculation:
      $B = 7 \times 7 = 49 \text{ ft}^2$

• Height of the Pyramid:

  • The height ($h$) is the perpendicular distance from the base to the apex.
  • In this example, the height is provided as 8 ft.

• Putting it All Together to Calculate Volume:

  • Substitute the values into the volume formula:
  • Base area ($B$) = 49 ft²
  • Height ($h$) = 8 ft
  • Volume calculation:
    $V = \frac{1}{3} Bh = \frac{1}{3} \times 49 \times 8$

• Final Volume Result:

  • Calculating the above gives:
  • $V = \frac{392}{3} \text{ ft}^3$

• Units for Volume:

  • The volume is expressed in cubic units (3rd power) corresponding to the units of measure for the base and height. In this case, we use cubic feet (ft³).