Answer :

Let side-length of the cube be x.

Then,

Volume of cube = (side)^{3}

= x^{3}

Total Surface Area of cube = 6(side)^{2}

= 6x^{2}

Given, the length of a cube is increased by 10% and its breadth is decreased by 10%.

∴ New length = x + 10% of x

= 1.1x

And, New Breadth = x - 10% of x

= 0.9x

∴ Volume of the new cuboid = l×b×h

= 1.1x× 0.9x × x

= 0.99 x^{3}

∴ Surface Area of the new cuboid = 2 × (lb + bh+ hl)

= 2 × (1.1x × 0.9x + 0.9x× x + x × 1.1x)

= 2 × (0.99x^{2} + 0.9x^{2} + 1.1x^{2})

= 2 × 2.99x^{2}

= 5.98x^{2} m^{2}

Percentage change in the volume =

= -0.01×100

= -1% (decrease)

Percentage change in the Surface Area

= -0.02×100

= -2% (decrease)

Hence, Volume decreases by 1% and Surface Area decreases by 2%.

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