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: V1=l×w×h=6 ft×3 ft×5 ft=90 ft3V_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: V2=l×w×h=5 ft×1 ft×7 ft=35 ft3V_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: V3=l×w×h=11 ft×8 ft×5 ft=440 ft3V_3 = l \times w \times h = 11 \text{ ft} \times 8 \text{ ft} \times 5 \text{ ft} = 440 \text{ ft}^3

  • Total Volume: V<em>total=V</em>1+V<em>2+V</em>3=90 ft3+35 ft3+440 ft3=565 ft3V<em>{\text{total}} = V</em>1 + V<em>2 + V</em>3 = 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 ft3565 \text{ ft}^3.