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

Question

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.

Answer 1

Step 1:

(a)

Side of a cube is 30 cm.

Error in measuring side of a square is 0.1 cm.

Let be the side of the square.

Volume of the square .

Apply derivative on each side.

Maximum possible error in the volume of the cube is .

Relative error in the volume of the cube is

Relative error in the volume of the cube is .

Percentage error in the volume of the cube is

Percentage error in the volume of the cube is .

Solutions:

(a)

Maximum possible error in the volume of the cube is .

Relative error in the volume of the cube is .

Percentage error in the volume of the cube is .

Answer 2

Step 1:

(b)

Surface area of the square .

Apply derivative on each side.

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

Relative error in the volume of the cube is

Relative error in the Surface area of the cube is .

Percentage error in the Surface area of the cube is

Percentage error in the Surface area of the cube is .

Solutions:

(b)

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

Relative error in the Surface area of the cube is

Percentage error in the Surface area of the cube is .