Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A packaging company is designing a new rectangular box. The box has dimensions of 5 cm by 4 cm by 3 cm. What is the surface area of this box?
- A120 cm²
- B47 cm²
- C30 cm²
- D94 cm²
Show answer & explanationAnswer & explanation
Correct answer: D. 94 cm²
A rectangular box (rectangular prism) has 6 faces. For dimensions length (L), width (W), and height (H), the surface area (SA) is given by the formula SA = 2(LW + LH + WH). Given L=5, W=4, H=3: SA = 2 * ((5*4) + (5*3) + (4*3)) = 2 * (20 + 15 + 12) = 2 * (47) = 94 cm².
Why the other options are wrong
- A. This is 4 times the volume, or 2 times the product of two largest faces.
- B. This is half of the correct surface area (LW + LH + WH).
- C. This is the volume of the box, not the surface area.
Surface Area of a Rectangular Prism
The total area of all the faces (surfaces) that enclose a rectangular prism (box).
- A rectangular prism has 6 faces (3 pairs of identical faces).
- Formula: SA = 2(LW + LH + WH), where L=length, W=width, H=height.
- Units are square units (e.g., cm², m²).
Memory trick: Unfold the box, count all the sides, sum their areas, where the surface hides!