5003 Praxis Practice Test Practice Question
Right rectangular prism P has height x, length y, and width Right rectangular prism has height 2x. length 2y, and width 22. Which TWO of the following statements must be true?
Correct Answer: B,E
Rationale: To analyze the surface area and volume of the prisms, we start with the formulas:
- Surface area of a prism = 2(lw + lh + wh)
- Volume of a prism = lwh
For prism P with dimensions \(x\), \(y\), and \(z\), the surface area is \(2(xy + xz + yz)\) and the volume is \(xyz\). Prism Q has dimensions \(2x\), \(2y\), and \(22\).
Calculating surface area for Q yields \(2(2x \cdot 2y + 2x \cdot 22 + 2y \cdot 22) = 4 \times \text{(surface area of P)}\), confirming option B as true.
For volume, \(V_Q = 2x \cdot 2y \cdot 22 = 88xy\) while \(V_P = xyz\). Since \(z\) is unspecified, we cannot definitively conclude that volume Q is 6 times volume P, making option D incorrect. However, since \(2x \cdot 2y \cdot 2z = 8xyz\), option E is validated.
Thus, B and E are the only statements that must be true. Options A, C, and D are incorrect due to miscalculations in the ratios of surface area and volume.
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