A solid cube has volume $(1000\pm 0.3)$ $cm^3$. The side of the cube is
- $(10\pm 0.1)$ $cm$
- $(10\pm 0.01)$ $cm$
- $(10\pm 0.001)$ $cm$
- $(10\pm 0.003)$ $cm$
Reveal answer
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C
Correct answer
Explanation
Volume V = s^3 = 1000. s = 10. Using error propagation, dV = 3 * s^2 * ds. 0.3 = 3 * 100 * ds, so ds = 0.3 / 300 = 0.001. Thus, s = 10 +/- 0.001.
AI explanation
The volume of a cube is the side length cubed, so the nominal volume of 1000 cm^3 gives a nominal side length of the cube root of 1000, which is 10 cm. Using the approximation for small errors, the fractional error in the volume equals 3 times the fractional error in the side length. This gives 0.3 divided by 1000 equals 3 times the error in the side length divided by 10. Solving this equation yields an error of 0.001 cm, making the side of the cube 10 plus or minus 0.001 cm.