Question

Each edge of a cube is increases by 50%. Find the percentage increase in the surface of area of the cube.

Answer 1

The percentage increase in the surface of area of the cube is 125%.

To find : The percentage increase in the surface of area of the cube.

Given :

Each edge of a cube is increases by 50%.

Consider the edge of a cube be x cm.

It increases by 50% = x + $\frac{x}{2}$ = $\frac{3x}{2}$

Formula used :

Total surface area = $6a^2$

Total surface area of original cube = $6x^2$

Here, $x$ = $\frac{3x}{2}$

Substituting the value of "a" in the formula we get,

Total surface area of a new cube = $6a^2$ = $6\times\ (\frac{3x}{2})^2$ = $6\times\frac{9x^2}{4}$ = 13.5 $x^2$

Increase in area = Total surface area of a new cube - Total surface area of original cube

                           = 13.5 $x^2$ - $6x^2$

                           = 7.5 $x^2$

Increase % of 7.5 $x^2$ = $\frac{7.5 x^2}{6x^2}\times100$ = 125%

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

To learn more...

1. If each side of a cube is increased by 50% find the percentage increase in its surface area

brainly.in/question/2177913      

2. Each edge of the cube is increased by 50% find the percentage increase in the surface area if the side of the cube is 4 cm

brainly.in/question/6266958