2022 · Q83
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?
Elementary MathematicsMensuration
- A17/20
- B17/40
- C7/10
- D9/10
Explanation
1/x+1/y+1/z = (xy+yz+zx)/xyz = 170/400 = 17/40, since 2(xy+yz+zx) = 340 and xyz = 400. This is the familiar identity 1/x+1/y+1/z = (xy+yz+zx)/xyz. The keyed option is B.