Suppose the length of a cube is increased by 10% and its breadth is decreased by 10%. Will the volume of the new cuboid be the same as that of the cube? What about the total surface areas? If they change, what would be the percentage change in both the cases?

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%.