Questions: What is the surface area of the right rectangular prism? Show your work.

What is the surface area of the right rectangular prism? Show your work.
Transcript text: What is the surface area of the right rectangular prism? Show your work.
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Solution

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Solution Steps

Step 1: Identify the dimensions of the rectangular prism

The given dimensions of the right rectangular prism are:

  • Length (l) = 15 cm
  • Width (w) = 10 cm
  • Height (h) = 7 cm
Step 2: Understand the formula for surface area

The surface area (SA) of a right rectangular prism is calculated using the formula: \[ SA = 2lw + 2lh + 2wh \]

Step 3: Substitute the dimensions into the formula

Substitute the given dimensions into the formula: \[ SA = 2(15 \, \text{cm} \times 10 \, \text{cm}) + 2(15 \, \text{cm} \times 7 \, \text{cm}) + 2(10 \, \text{cm} \times 7 \, \text{cm}) \]

Step 4: Calculate each term

Calculate each term separately: \[ 2(15 \times 10) = 2(150) = 300 \, \text{cm}^2 \] \[ 2(15 \times 7) = 2(105) = 210 \, \text{cm}^2 \] \[ 2(10 \times 7) = 2(70) = 140 \, \text{cm}^2 \]

Step 5: Sum the calculated terms

Add the calculated terms to find the total surface area: \[ SA = 300 \, \text{cm}^2 + 210 \, \text{cm}^2 + 140 \, \text{cm}^2 = 650 \, \text{cm}^2 \]

Final Answer

The surface area of the right rectangular prism is \( 650 \, \text{cm}^2 \).

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