Question

The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 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

Answer:

A) Maximum error = 36 cm²

B) Relative Error = 0.0267

C) percentage error = 2.67%

Step-by-step explanation:

Surface area of the cube is;

A(x) = 6x²

Where x is the length of the edge of the cube.

dA/dx = 12x

When x is small like in this case, we can write;

ΔA/Δx ≈ 12x

Thus, ΔA ≈ 12x•Δx

A) Maximum error = 12*15*0.2

Maximum error = 36 cm²

B) Relative Error = Max Error/Surface Area

Surface area = 6 x 15² = 1350

Thus,relative error = 36/1350

Relative Error = 0.0267

C) percentage error = Relative Error x 100%

percentage error = 0.0267 x 100%

percentage error = 2.67%

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