Volume of Solid Figures

Finding the Volume of a Solid Figure

• To find the volume of a solid figure, one must identify the dimensions (length, width, and height) of the figure.

• Example:

  • Consider a complex solid figure composed of multiple rectangular prisms.

  • The figure has the following dimensions:

    • Section 1: Length = 6 ft, Width = 3 ft, Height = 5 ft
    • Section 2: Length = 5 ft, Width = 1 ft, Height = 7 ft
    • Section 3: Length = 11 ft, Width = 8 ft, Height = 5 ft

• To find the total volume, calculate the volume of each section separately and then add them together.

  • Volume of Section 1: V_1 = l \times w \times h = 6 \text{ ft} \times 3 \text{ ft} \times 5 \text{ ft} = 90 \text{ ft}^3
  • Volume of Section 2: V_2 = l \times w \times h = 5 \text{ ft} \times 1 \text{ ft} \times 7 \text{ ft} = 35 \text{ ft}^3
  • Volume of Section 3: V_3 = l \times w \times h = 11 \text{ ft} \times 8 \text{ ft} \times 5 \text{ ft} = 440 \text{ ft}^3

• Total Volume: V{\text{total}} = V1 + V2 + V3 = 90 \text{ ft}^3 + 35 \text{ ft}^3 + 440 \text{ ft}^3 = 565 \text{ ft}^3

• The total volume of the solid figure is 565 \text{ ft}^3.