Math Problem Statement

What is the volume and surface area of a rectangular prism with dimensions L = 13 mm, W = 9 mm, and H = 5 mm, and another prism with dimensions L = 15 cm, W = 3 cm, and H = 12 cm?

Solution

The image contains calculations related to rectangular prisms, including volume and surface area computations. Here's an analysis and breakdown:


Volume Calculation

The formula for the volume of a rectangular prism is: V=L×W×HV = L \times W \times H From the image:

  • L=13mmL = 13 \, \text{mm},
  • W=9mmW = 9 \, \text{mm},
  • H=5mmH = 5 \, \text{mm}.

The volume calculation shown is: V=13×9×5=585mm3.V = 13 \times 9 \times 5 = 585 \, \text{mm}^3.

This calculation is correct.


Surface Area Calculation

The formula for the surface area (SASA) of a rectangular prism is: SA=2(LW+LH+WH)SA = 2(LW + LH + WH) Breaking it into components:

  1. LW=13×9=117mm2LW = 13 \times 9 = 117 \, \text{mm}^2,
  2. LH=13×5=65mm2LH = 13 \times 5 = 65 \, \text{mm}^2,
  3. WH=9×5=45mm2WH = 9 \times 5 = 45 \, \text{mm}^2.

Substituting: SA=2(117+65+45)=2(227)=454mm2.SA = 2(117 + 65 + 45) = 2(227) = 454 \, \text{mm}^2.

However, in the image, the surface area is listed as 494 mm². This discrepancy suggests that an additional value may have been added incorrectly. The correct surface area should be 454 mm².


Second Volume Calculation

For the prism with:

  • L=15cmL = 15 \, \text{cm},
  • W=3cmW = 3 \, \text{cm},
  • H=12cmH = 12 \, \text{cm},

The volume is calculated as: V=L×W×H=15×3×12=540cm3.V = L \times W \times H = 15 \times 3 \times 12 = 540 \, \text{cm}^3.

This calculation is also correct.


Key Observations:

  1. Volume calculations are accurate.
  2. There may be an error in the surface area computation for the first prism.

Would you like me to:

  1. Recalculate surface area step-by-step for clarification?
  2. Explain formulas for related 3D shapes?
  3. Discuss real-life applications of these calculations?
  4. Show how to double-check calculations for errors?
  5. Provide tips for organizing geometry solutions?

Tip: Always double-check calculations by substituting intermediate results into the formula.

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Math Problem Analysis

Mathematical Concepts

Volume of rectangular prisms
Surface area of rectangular prisms

Formulas

Volume: V = L × W × H
Surface Area: SA = 2(LW + LH + WH)

Theorems

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Suitable Grade Level

Grades 6-8