Question

The surface area of a rectangular prism is 60. Which of the following are possible dimensions of the rectangular prism? 1 Pt

Answer 1

The surface area of a rectangular prism with sides a, b and c is given by the formula:

$S=2(ab+ac+bc)$

Use that formula to find the surface area that a prism with the given dimensions on each option would have.

A. 6, 2, 1 1/2

$\begin{gathered} S=2(6\cdot2+6\cdot1\frac{1}{2}+2\cdot1\frac{1}{2}) \\ =2(12+9+3) \\ =2(24) \\ =48 \end{gathered}$

B. 5, 4, 1 1/4

$\begin{gathered} S=2(5\cdot4+5\cdot1\frac{1}{4}+4\cdot1\frac{1}{4}) \\ =2(20+\frac{25}{4}+5) \\ =2(\frac{125}{4}) \\ =\frac{125}{2} \\ =62.5 \end{gathered}$

C. 3, 4, 1 1/2

$\begin{gathered} S=2(3\cdot4+3\cdot1\frac{1}{2}+4\cdot1\frac{1}{2}) \\ =2(12+3\frac{3}{2}+6) \\ =2(21\frac{3}{2}) \\ =45 \end{gathered}$

D. 6, 3, 1 1/3

$\begin{gathered} S=2(6\cdot3+6\cdot1\frac{1}{3}+3\cdot1\frac{1}{3}) \\ =2(18+8+4) \\ =2(30) \\ =60 \end{gathered}$

Therefore, the only possible dimensions of a rectangular prism with surface area 60 listed on the options, are 6, 3 and 3 1/3. The answer is:

$\text{Option D}$