Let x, y, z be the length, breadth, height of a cuboid. If its volume is 400 cubic cm and total surface area is 340 square cm, then what is x^{-1}+y^{-1}+z^{-1} equal to?
- A. \frac{17}{20}
- B. \frac{17}{40} ✓
- C. \frac{7}{10}
- D. \frac{9}{10}
Correct Answer: B. \frac{17}{40}
Explanation
Volume V = xyz = 400 and total surface area S = 2(xy+yz+zx) = 340 \implies xy+yz+zx = 170. The required expression is \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{xy+yz+zx}{xyz} = \frac{170}{400} = \frac{17}{40}.
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