Question

The edge of a cube was found to be 15 cm with a possible error in measurement of 0.5 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.) (a) the volume of the cube maximum possible error cm3 relative error percentage error % (b) the surface area of the cube maximum possible error cm2 relative error percentage error

Answer 1

Answer: maximum error = 90cm^2

Relative error = 0.067

Percentage error = 6.7%

Explanation:

Given:

Size of edge of the cube = 15cm

Margin of error = 0.5cm

Therefore:

We all know a cube has 6 equals sides

A (x) = 6x^2

Differentiate

dA/dx = 12x

When change in x ( dx ) is small like in the case above

dA/dx = 12

dA = 12 x dx

1. Maximum error

= 12 x 15 x 0.5

= 90cm^2

2. Relative error = Max error / surface area

= 90 / 6 x 15^2

= 0.067

3. Percentage error = relative error x 100

= 0.067 x 100

= 6.7%