17. A right rectangular prism has length 5.0 centimeters, width 7.3 centimeters, and height 9.2 centimeters. What is the surface area in square centimeters, of the prism?
Answer: C
The surface area of the right rectangular prism is 299.32 square centimeters.
To find the surface area of a right rectangular prism, the formula used is \(2(lw + lh + wh)\). Substituting the given dimensions, we calculate the surface area as \(2(5.0 \times 7.3 + 5.0 \times 9.2 + 7.3 \times 9.2) = 299.32\) square centimeters.
A) 149.66
Option A is incorrect as it does not align with the calculated surface area. The value of 149.66 could represent half of the surface area or an incorrect calculation of one of the components involved in the formula.
B) 167.9
Option B is also incorrect. This value does not reflect the total surface area calculated using the dimensions provided. It may arise from miscalculating one or more of the products in the surface area formula.
C) 299.32
Option C is correct as it accurately represents the total surface area of the prism when calculated using the given dimensions. The calculation confirms that this value is derived from the correct application of the surface area formula for a rectangular prism.
D) 335.18
Option D is incorrect. This figure may result from an error in the calculations, possibly from misapplying the formula or erroneous arithmetic. The surface area cannot exceed the calculated value of 299.32 given the specified dimensions.
Conclusion
The correct answer, 299.32 square centimeters, is achieved through a precise application of the surface area formula for a right rectangular prism. All other options fail to represent valid computations based on the prism's dimensions, either by underestimating or overestimating the total surface area.