Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A manufacturer is designing a new packaging box for a product. The box needs to be a rectangular prism with dimensions of 6 inches by 4 inches by 3 inches. If the box is to be covered entirely with a decorative paper, what is the total surface area of the box that needs to be covered?
- A74 square inches
- B148 square inches
- C108 square inches
- D72 square inches
Show answer & explanationAnswer & explanation
Correct answer: B. 148 square inches
The surface area of a rectangular prism is given by the formula SA = 2(lw + lh + wh), where l is length, w is width, and h is height. This represents the sum of the areas of all six faces of the prism.
Why the other options are wrong
- A. This is incorrect; it might be the sum of only three faces or a miscalculation.
- C. This is incorrect; it might be a result of adding dimensions or an incorrect formula application.
- D. This is incorrect; it is the volume of the box, not the surface area.
Surface Area of Rectangular Prism
The total area of all the faces (surfaces) of a three-dimensional rectangular prism.
- A rectangular prism has 6 faces (3 pairs of identical rectangular faces).
- Formula: SA = 2(lw + lh + wh).
- Where l=length, w=width, h=height.
Memory trick: Surface Area: 'Two' of 'Length-Width', 'Length-Height', and 'Width-Height'!