Example Question - 3d figure
Here are examples of questions we've helped users solve.
Calculating Volume of Composite 3D Figure
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 cm Calculate the volume (V₁) of the first prism: V₁ = l₁ × w₁ × h₁ V₁ = 9.1 cm × (2.4 cm + 4.7 cm + 2.4 cm) × 2.4 cm V₁ = 9.1 cm × 9.5 cm × 2.4 cm V₁ = 9.1 cm × 22.8 cm V₁ = 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 cm Calculate the volume (V₂) of the cut-out section: V₂ = l₂ × w₂ × h₂ V₂ = 4.7 cm × 2.4 cm × 2.4 cm V₂ = 11.328 cm³ Now subtract V₂ from V₁ to get the total volume (V) of the composite figure: V = V₁ - V₂ V = 207.48 cm³ - 11.328 cm³ V ≈ 196.152 cm³ Round to the nearest hundredth, if necessary: V ≈ 196.15 cm³ So, the volume of the composite figure is approximately 196.15 cubic centimeters.
Determining Planes Containing Line Segment DH in a 3D Figure
The image shows a question that asks for two different planes that contain the line segment DH in a three-dimensional figure, which is described as a rectangular shipping box. Without the actual visual of the figure, I cannot determine the exact position of the line segment DH or identify the planes it lies on. However, based on typical conventions for naming points in a rectangular prism or box, DH would likely be a line segment on one of the edges of the box. To answer a question like this, one would generally look for two planes that share this line segment. For example, if D and H were opposite corners on the top surface of the box, then plane ADH (including one adjacent side) and plane HDG (including the other adjacent side) would contain DH. This is just a general description and can't be confirmed without seeing the specific figure. Given the choice options: A) Plane ADE, Plane CGH B) Plane ADE, Plane FBC C) Plane ADC, Plane CGH D) Plane FBC, Plane ADC Without the figure, these choices do not provide enough context to determine which two planes contain DH. Please provide the visual of the box, or additional information so I can help you determine the correct answer.
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