Question

If each side of a cube increases 50% by length, then what is the parcentage increase in total
surface area of the cube?​

Answer 1

Let x be the edge of a cube.

Surface area of the cube having edge x = 6x2 ………..(1)

As given, a new edge after increasing the existing edge by 50%, we get

The new edge = x + 50 x /100

The new edge = = 3x/2

Surface area of the cube having edge 3x/2 = 6 x (3x/2)2= (27/2)x2……..(2)

Subtract equation (1) from (2) to find the increase in the Surface Area:

Increase in the Surface Area = (27/2)x2 – 6x2

Increase in the Surface Area = = (15/2)x2

Now,

Percentage increase in the surface area = ((15/2)x2 / 6x2) x 100

= 15/12 x 100

= 125%

Therefore, the percentage increase in the surface area of a cube is 125.

Answer 2

Answer:

$the \: sides \: of \: the \: cube = 100 \: unit$

$the \: total \: surface \: of \: the \: cube = 6 \times {l}^{2}$

$if \: we \: increase \: 100 \: by \: 50\% \: we \: will \: get \: = 150 \: unit$

$the \: area \: will \: be = 6 \times (150 {}^{2} )$

$= 6 \times 22500$

$= 135000 \: unit {}^{2}$

$the \: older \: area \: would \: be \: = 6 \times ( {100}^{2} )$

$= 10000 \: unit {}^{2}$

$the \: increase \: of \: area = (135000 - 60000) = 75000 \: unit {}^{2}$

$in \: 10000 \: the \: increase \: is \: = 75000 \\ in \: 1 \: the \: increase \: is \: = \frac{75000}{10000} \\ in \: 100 \: the \: increase \: is \: = \frac{75000 \times 100}{10000}$

$= 750\%$