Math Problem Statement

What is the volume

What is the volume?

Solution

The shape in the image appears to be a combination of two rectangular prisms stacked on top of each other. To find the total volume, we need to calculate the volume of each prism separately and then add them together.

Top Prism (Region A):

  • Dimensions: 5 ft (length) × 2 ft (height) × 3 ft (width)
  • Volume of top prism VA=length×width×height=5×3×2=30cubic feetV_A = \text{length} \times \text{width} \times \text{height} = 5 \times 3 \times 2 = 30 \, \text{cubic feet}

Bottom Prism (Region B):

  • Dimensions: 5 ft (length) × 3 ft (height) × 6 ft (width)
  • Volume of bottom prism VB=length×width×height=5×6×3=90cubic feetV_B = \text{length} \times \text{width} \times \text{height} = 5 \times 6 \times 3 = 90 \, \text{cubic feet}

Total Volume:

Vtotal=VA+VB=30+90=120cubic feetV_{\text{total}} = V_A + V_B = 30 + 90 = 120 \, \text{cubic feet}

So, the total volume of the shape is 120 cubic feet.

Would you like more details or have any questions? Here are five related questions to explore further:

  1. How would the volume change if the dimensions of the top prism were doubled?
  2. What is the surface area of the entire shape?
  3. How would the calculation change if the two regions were cylinders instead of rectangular prisms?
  4. If this structure were filled with water, how many gallons could it hold? (Hint: 1 cubic foot = ~7.48 gallons)
  5. Can you think of real-world objects or structures that have similar shapes?

Tip: To calculate the volume of composite shapes, break them down into simpler components (like rectangular prisms), find the individual volumes, and sum them up.

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Math Problem Analysis

Mathematical Concepts

Volume of Rectangular Prisms
Geometry
Composite Shapes

Formulas

Volume of a rectangular prism = length × width × height

Theorems

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Suitable Grade Level

Grades 6-8