Question

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is?

A 2.5%
B 3.5%
C 4.5%
D 6%

Answer 1

The maximum error in determining the density of a cube, given a 1.5% error in mass and 1% error in measuring the sides, is 4.5%.

Step-by-step explanation:

The density of a material can be found by dividing its mass by its volume.

In the case of a cube, volume is found by cubing the side length (Volume = side³). If there is a relative error of 1.5% in the measurement of the mass and 1% in the measurement of each side of the cube, the total relative error in density can be calculated by adding these errors.

Since volume is computed by cubing the side length, you must triple the error for the side length measurement.

Total relative error in density = Error in mass + 3(Error in side length)

= 1.5% + 3(1%)

= 1.5% + 3%

= 4.5%.

Therefore, the maximum error in determining the density using these measurements would be 4.5%.