Answer :

Let side-length of the cube be x.


Then,


Volume of cube = (side)3


= x3


Total Surface Area of cube = 6(side)2


= 6x2


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 x3


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


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


= 2 × (0.99x2 + 0.9x2 + 1.1x2)


= 2 × 2.99x2


= 5.98x2 m2


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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