Which expression represents the surface area of the prism?
Understand the Problem
The question is asking for the expression that represents the surface area of a right rectangular prism given its dimensions. The dimensions are 3, 5, and 6, and the surface area can be calculated using the formula for the surface area of a rectangular prism.
Answer
$$ 2 \cdot (15 + 30 + 18) $$
Answer for screen readers
The expression representing the surface area of the prism is: $$ 2 \cdot (15 + 30 + 18) $$
Steps to Solve
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Identify the Surface Area Formula The surface area $S$ of a right rectangular prism can be calculated using the formula: $$ S = 2(lw + lh + wh) $$ where $l$, $w$, and $h$ are the length, width, and height of the prism.
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Substitute the Dimensions Substituting the dimensions into the formula, we have:
- Length $l = 5$
- Width $w = 3$
- Height $h = 6$
The surface area becomes: $$ S = 2(5 \cdot 3 + 5 \cdot 6 + 3 \cdot 6) $$
- Calculate Each Area Component Calculate each term within the parentheses:
- $lw = 5 \cdot 3 = 15$
- $lh = 5 \cdot 6 = 30$
- $wh = 3 \cdot 6 = 18$
So, we update the surface area expression to: $$ S = 2(15 + 30 + 18) $$
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Simplify the Expression Inside the Parentheses Now, add up the values inside the parentheses: $$ 15 + 30 + 18 = 63 $$
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Final Calculation Now, multiply by 2: $$ S = 2 \cdot 63 = 126 $$
Thus, the surface area is: $$ S = 126 $$
The equivalent expression reflecting this calculation is: $$ S = 2(15 + 30 + 18) $$
The expression representing the surface area of the prism is: $$ 2 \cdot (15 + 30 + 18) $$
More Information
The total surface area calculated is $126$ square units. The surface area formula accounts for all six faces of the prism, ensuring accurate measurement for geometric calculations.
Tips
- Forgetting to multiply the combined area by 2, which is necessary to account for both pairs of opposite faces.
- Not recognizing that dimensions must be multiplied in pairs to determine the area of the faces properly.
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