Calculate Surface Area: 3×5×2 Rectangular Prism Problem

Calculate the surface area of the orthohedron below using the data in the diagram.

To solve this problem, we'll utilize the formula for the surface area of a cuboid. The steps are as follows:

• Step 1: Identify the dimensions from the problem. The dimensions provided are $a = 3$, $b = 5$, and $c = 2$.
• Step 2: Apply the surface area formula for a cuboid. The formula is: $2(ab + bc + ac)$ where $a$, $b$, and $c$ are the dimensions of the cuboid.
• Step 3: Substitute the known values into the formula: $2(3 \cdot 5 + 5 \cdot 2 + 3 \cdot 2)$
• Step 4: Calculate each term inside the parentheses: - $a \cdot b = 3 \cdot 5 = 15$ - $b \cdot c = 5 \cdot 2 = 10$ - $a \cdot c = 3 \cdot 2 = 6$
• Step 5: Sum the results from Step 4: $15 + 10 + 6 = 31$
• Step 6: Multiply the sum by 2 to find the total surface area: $2 \times 31 = 62$

Thus, after performing the necessary calculations, the surface area of the orthohedron is $62$ square units.