Question - Calculating Volume of Composite 3D Figure
Solution:
To find the volume of the composite figure in the image, consider it as two separate rectangular prisms and then add their volumes together.**First rectangular prism:**The dimensions of the larger prism include the entire length, width, and height of the figure.- Length (l₁) = 9.1 cm- Width (w₁) = 2.4 cm + 4.7 cm + 2.4 cm- Height (h₁) = 2.4 cmCalculate the volume (V₁) of the first prism:V₁ = l₁ × w₁ × h₁V₁ = 9.1 cm × (2.4 cm + 4.7 cm + 2.4 cm) × 2.4 cmV₁ = 9.1 cm × 9.5 cm × 2.4 cmV₁ = 9.1 cm × 22.8 cmV₁ = 207.48 cm³**Second rectangular prism (the cut-out section):**The dimensions of the cut-out are given inside the larger prism.- Length (l₂) = 4.7 cm- Width (w₂) = 2.4 cm- Height (h₂) = 2.4 cmCalculate the volume (V₂) of the cut-out section:V₂ = l₂ × w₂ × h₂V₂ = 4.7 cm × 2.4 cm × 2.4 cmV₂ = 11.328 cm³Now subtract V₂ from V₁ to get the total volume (V) of the composite figure:V = V₁ - V₂V = 207.48 cm³ - 11.328 cm³V ≈ 196.152 cm³Round to the nearest hundredth, if necessary:V ≈ 196.15 cm³So, the volume of the composite figure is approximately 196.15 cubic centimeters.
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