Discussion
The volume of a cube is 2197 cm3. What is its lateral surface area (in cm2)?
Answer: A
The lateral surface area is 676 cm2.
The side of the cube is the cube root of its volume, and the lateral surface is the four side faces.
\[ \begin{aligned} a &= \sqrt[3]{2197} = 13 \text{ cm} \\ \text{LSA} &= 4a^{2} = 4 \times 169 = 676 \end{aligned} \]
1014 is the total surface area, \(6a^{2}\), which includes the top and bottom; the question asks for the lateral area only. 845 is \(5a^{2}\), and 576 is \(4 \times 12^{2}\), using the wrong side.
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