Subjects geometry

Stepped Solid Volume 3B00A7

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Question: What is the volume of this figure?\n\n2 cm\n5 cm\n2 cm\n3 cm\n6 cm\n\ncubic centimeters\n\nA blue stepped 3D solid is shown in the center-left; its labeled dimensions are 2 cm on the top front edge, 5 cm on the right slanted edge, 2 cm on the left vertical edge, 3 cm on the left slanted depth edge, and 6 cm on the bottom front edge.
1. **State the problem:** We need to find the volume of a stepped 3D solid with given dimensions: top front edge $2$ cm, right slanted edge $5$ cm, left vertical edge $2$ cm, left slanted depth edge $3$ cm, and bottom front edge $6$ cm.\n\n2. **Analyze the shape:** The figure can be divided into two rectangular prisms stacked in a stepped manner.\n\n3. **Identify dimensions of each prism:**\n- Bottom prism: length $6$ cm, width $3$ cm (depth), height $2$ cm (left vertical edge).\n- Top prism: length $2$ cm, width $3$ cm (same depth as bottom), height $2$ cm (top front edge height).\n\n4. **Volume formula for a rectangular prism:**\n$$V = \text{length} \times \text{width} \times \text{height}$$\n\n5. **Calculate volume of bottom prism:**\n$$V_1 = 6 \times 3 \times 2 = 36$$\n\n6. **Calculate volume of top prism:**\n$$V_2 = 2 \times 3 \times 2 = 12$$\n\n7. **Total volume:**\n$$V = V_1 + V_2 = 36 + 12 = 48$$\n\n8. **Answer:** The volume of the figure is $48$ cubic centimeters.
\n\n\n\n\n\n6 cm\n2 cm\n3 cm\n5 cm\n2 cm\n