A cube has a surface area of 5400square units. Its volume would increase approximately _______ if the side is increased by 5units.

Let the initial side of the cube be a.
The total surface area of a cube is given by 6a
2
.

6a
2
=5400
a
2
=900⟹a=30units
The initial volume (V
1
​
) is:

V
1
​
=a
3
=30
3
=27000cubic units
If the side is increased by 5units, the new side (a
′
) is:

a
′
=30+5=35units
The new volume (V
2
​
) is:

V
2
​
=(a
′
)
3
=35
3
=42875cubic units
The increase in volume is:

ΔV=V
2
​
−V
1
​
=42875−27000=15875cubic units
The percentage increase in volume is:

Percentage Increase=
V
1
​

ΔV
​
×100=
27000
15875
​
×100=
270
15875
​
≈58.79%≈59%