Question

The edge of a cube was found to be 15 cm with a possible error in measurement of 0.4 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.)

Answer 1

11

Explanation:

Answer 2

 The maximum error on volume = 270cm³

The relative error on the volume =0.08

The percentage error on volume = 8%.

How to calculate the volume of a given cube?

To calculate the volume of a given cube, the following steps should be taken as follows:

Formula for volume of a cube = a³

where;

a = 15 cm

Volume(V) = 15³ = 3375cm³

The maximum error on volume(dV);

= 3×side²×dx

= 3×15²×0.4cm

= 270cm³

The relative error on the volume;

= dV/V

= 270/3375

= 0.08

The percentage error on volume;

=Relative error × 100

= 0.08× 100

= 8%