Step 1:

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(a)

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Side of a cube is 30 cm.

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Error in measuring side of a square is 0.1 cm.

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Let $\"\"$ be the side of the square.

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Volume of the square $\"\"$ .

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Apply derivative on each side.

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$\"\"$

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$\"\"$

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Maximum possible error in the volume of the cube is $\"\"$ .

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Relative error in the volume of the cube is $\"\"$

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$\"\"$

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Relative error in the volume of the cube is $\"\"$ .

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Percentage error in the volume of the cube is $\"\"$

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$\"\"$

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Percentage error in the volume of the cube is $\"\"$ .

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Step 2:

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(b)

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Surface area of the square $\"\"$ .

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Apply derivative on each side.

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$\"\"$

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$\"\"$

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Maximum possible error in the Surface area of the cube is $\"\"$ .

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Relative error in the volume of the cube is $\"\"$

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$\"\"$

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Relative error in the Surface area of the cube is $\"\"$ .

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Percentage error in the Surface area of the cube is $\"\"$

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$\"\"$

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Percentage error in the Surface area of the cube is $\"\"$ .

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Solutions:

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(a)

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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 $\"\"$ .

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(b)

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Maximum possible error in the Surface area of the cube is $\"\"$ .

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Relative error in the Surface area of the cube is $\"\"$

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Percentage error in the Surface area of the cube is $\"\"$ .