Math Problem Statement

Find the surface area of the rectangular prism with dimensions 8 cm, 9 cm, and 13 cm.

Solution

The problem asks for the surface area of a rectangular prism. The dimensions of the prism provided in the image are:

  • Length = 8 cm
  • Width = 9 cm
  • Height = 13 cm

The formula for the surface area SS of a rectangular prism is:

S=2(lw+lh+wh)S = 2(lw + lh + wh)

Where:

  • ll is the length,
  • ww is the width,
  • hh is the height.

Let's calculate the surface area:

S=2(8×9+8×13+9×13)S = 2(8 \times 9 + 8 \times 13 + 9 \times 13)

Now, I'll compute this.The surface area of the rectangular prism is 586cm2586 \, \text{cm}^2.

Would you like further details or have any additional questions?

Here are five related questions:

  1. How do you calculate the volume of this rectangular prism?
  2. What would the surface area be if one of the dimensions changed?
  3. How do the surface area formulas differ for other 3D shapes like cylinders or spheres?
  4. How is surface area applied in real-world situations, such as packaging?
  5. How does surface area scale if all the dimensions are doubled?

Tip: Remember, surface area grows proportionally to the square of the dimensions, while volume grows proportionally to the cube!

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Rectangular Prisms

Formulas

Surface Area of Rectangular Prism: S = 2(lw + lh + wh)

Theorems

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Suitable Grade Level

Grades 6-8