To find the surface area of the right rectangular prism, we need to first identify the dimensions of the prism and then use the surface area formula for a rectangular prism.

Step 1: Determine the dimensions of the prism

• The smallest edge is given as 2 cm.
• The next greatest edge is twice the length of the smallest edge:
  $2 \times 2 \, \text{cm} = 4 \, \text{cm}$
• The greatest edge is three times the length of the smallest edge:
  $3 \times 2 \, \text{cm} = 6 \, \text{cm}$

So, the dimensions of the prism are 2 cm, 4 cm, and 6 cm.

Step 2: Calculate the surface area

The surface area $A$ of a rectangular prism is given by the formula: $A = 2lw + 2lh + 2wh$ where $l$, $w$, and $h$ are the lengths of the edges.

Here:

• $l = 2 \, \text{cm}$
• $w = 4 \, \text{cm}$
• $h = 6 \, \text{cm}$

Substitute the values into the formula: $A = 2(2 \times 4) + 2(2 \times 6) + 2(4 \times 6)$

$A = 2(8) + 2(12) + 2(24)$

$A = 16 + 24 + 48$

$A = 88 \, \text{cm}^2$

Final Answer

The surface area of the prism is 88 square centimeters.

Would you like more details or have any other questions?

Here are five related questions:

1. How do you find the volume of the same right rectangular prism?
2. If the smallest edge was doubled, how would the surface area change?
3. What is the length of the diagonal of this rectangular prism?
4. How do you derive the formula for the surface area of a rectangular prism?
5. How would the surface area change if each dimension was scaled by a factor of 3?

Tip: In problems involving geometric shapes, always identify all dimensions clearly before applying any formulas.