6 points scalcET8 3.10.033. The edge of a cube was found to be 30 cm with a poss

Question

6 points scalcET8 3.10.033. The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 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.) My Notes Ask Your Teache (a) the volume of the cube maximum possible error relative error percentage error cm3 (b) the surface area of the cube maximum possible error relative error percentage error cm2 Need Help? ReadIt Talk to a Tutor Watch It

Explanation / Answer

Solution:

a)

The volume of the cube

x = 30 cm ± 0.1 cm

v = x^3

dV/dx = 3x^2

dV = 3x^2 dx

dV = 3(30 cm)^2 (± 0.1cm)

dV = 3(900 cm^2) (± 0.1cm)

dV = 2700 cm^2 (± 0.1cm)

dV = ± 270 cm^3

Relative Error:Divide the error by the total volume:

dV/V = (±270cm^3/)/(30cm)^3

        = (±270cm^3)/(27,000cm^3)

      = 0.01

Percentage Error: multiply by 100:0.01*100 = 1%

(b)

A = 6x^2

dA/dx = 6(2x)

dA = 12x dx

dA = 12(30 cm)(±0.1 cm)

dA = ± 36cm^2

Relative Error : Divide the error by the total area:

dA/A = (±36cm^2)/(6(30cm)^2)

      = (±36cm^2)/(5,400cm^2)

        = 0.067

Percentage Error: multiply by 100: 0.0067*100 = 0.67%

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