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percentage error in volume of the cube and surface area of the cube.

0 votes
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 (a) the volume of the cube and (b) the surface area
of the cube.
asked Jan 22, 2015 in CALCULUS by anonymous

2 Answers

0 votes

Step 1:

(a)

Side of a cube is 30 cm.

Error in measuring side of a square is 0.1 cm.

Let image be the side of the square.

Volume of the square image.

Apply derivative on each side.

image

image

Maximum possible error in the volume of the cube is image.

Relative error in the volume of the cube is image

image

Relative error in the volume of the cube is image.

Percentage error in the volume of the cube is image

image

Percentage error in the volume of the cube is image.

Solutions:

(a)

Maximum possible error in the volume of the cube is image.

Relative error in the volume of the cube is image.

Percentage error in the volume of the cube is image.

answered Jan 22, 2015 by Lucy Mentor
0 votes

Step 1:

(b)

Surface area of the square image.

Apply derivative on each side.

image

image

Maximum possible error in the Surface area of the cube is image.

Relative error in the volume of the cube is image

image

Relative error in the Surface area of the cube is image.

Percentage error in the Surface area of the cube is image

image

Percentage error in the Surface area of the cube is image.

Solutions:

(b)

Maximum possible error in the Surface area of the cube is image.

Relative error in the Surface area of the cube is image

Percentage error in the Surface area of the cube is image.

answered Jan 22, 2015 by Lucy Mentor

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