1. If each edge of a cube is increased by 25%, then what is the percentage increase in its surface area?

  2. If the length of a rectangle is increased by 20% and breadth of the rectangle is increased by 30%, what is the new area percentage compared to original area percentage of this particular rectangle?

Please, can anyone explain the answer with logic and explanation? what is effective percentage, how can we calculate?

I have Tried this:

x+y+xy/100 using Formula, How this Formula Derived why we want to use this Formula Here

  • $\begingroup$ typically the new value x 100 / old value. for 1) c being the edge, old surface = 6 c², new surface = 6 x ( 1.25 c ) ² and then percentage = 6 x ( 1.25 c ) ² / 6 c² , ... etc $\endgroup$ – user354674 Aug 16 '16 at 5:40
  • $\begingroup$ Here is my hint to the op. The regular cube has edges of x, but the 25% more one has edges x+.25x $\endgroup$ – Erock Brox Aug 16 '16 at 5:59

For number 1: Make the edge of the cube $4$ and increase it by $25$ to get $5$ To find the surface area we do $(5^2)*6=150.$ The original cube's areas was $(4^2)*6=96.$ $96/150=0.64=64%$

For #2: Try to plug in a number and then solve.


We define relative change as the ratio of the actual increase (or decrease) to the original measurement.That is,

relative change $= \dfrac {(actual \quad increase)}{(original \quad measurement)} = \dfrac {(new \quad ...) – (original \quad ...)}{(original \quad ...) }$ .

To make the results more ease to compare, we express such relative change in percent. That is, percentage change $= … = \dfrac {(new \quad ...) – (original \quad ...)}{(original \quad ...) } \times 100 \%$.

Thus, we need to find:-

(1) the original length = x, say;

(2) the new length = 1.25x;

(3) the original total surface area of the 6-sided cube $= 6x^2$;

(4) the new total surface area of the 6-sided cube $= 6(1.25x)^2$.

Then, apply the formula. The x’s will be cancelled in the process of computation.

Q#2 can be done in the similar fashion.


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