Math Problem Statement

A rectangular prism has a length of 2 units, a width of 8 units, and a height of 6 units. What is the surface area?

Solution

Let us calculate the surface area of the rectangular prism given its dimensions: length l=2l = 2, width w=8w = 8, and height h=6h = 6.

Formula for Surface Area of a Rectangular Prism:

Surface Area=2(lw+lh+wh)\text{Surface Area} = 2(lw + lh + wh)

Step-by-Step Calculation:

  1. Calculate lwlw: lw=2×8=16lw = 2 \times 8 = 16

  2. Calculate lhlh: lh=2×6=12lh = 2 \times 6 = 12

  3. Calculate whwh: wh=8×6=48wh = 8 \times 6 = 48

  4. Add these values and multiply by 2: Surface Area=2(16+12+48)=2×76=152\text{Surface Area} = 2(16 + 12 + 48) = 2 \times 76 = 152

Final Answer:

The surface area of the rectangular prism is: 152units2\boxed{152 \, \text{units}^2}

This corresponds to the GRAY option.


Would you like further clarification or a breakdown of any specific part?

5 Related Questions:

  1. What is the volume of the same rectangular prism?
  2. How would the surface area change if the length was doubled?
  3. What is the relationship between surface area and volume in a rectangular prism?
  4. Can you derive the surface area formula from the basic area calculations of its faces?
  5. How would the surface area formula change for a cube (all sides equal)?

Tip:

Always verify the dimensions are substituted correctly in formulas to avoid calculation errors!

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Rectangular Prisms

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8