Question

Each Edge of a cube is increased by 50%.Find the percentage change in the area of cube.

Answer 1

Let the edge of cube be x
Surface area = 6x²
50% increased edge = x+ (50/100)× 100
= x+  x/2
= (2x+x)/2
= 3x/2
New area = 6(3x/2)²
= 6(9x²/4)
= 27x²/2
Change in areas = 27x²/2  - 6x²
= (27x² - 12x²)/2
= 15x²/2
5 change in areas = [(15x²/2)/6x²]× 100
= [15x²/12x²]× 100
= (15/12) × 100
= 125
% change in areas = 125%

Answer 2

Answer:

125 %

Step-By-Step Explanation:

In such questions, the first  step of all individuals should be assuming the side to be a variable.

Let the measure of each edge of the cube be ' x ' cm.

Total surface area of the cube = 6 ( x ) ^ 2

Total surface area of the cube = 6 * x ^ 2

Total surface area of the cube = 6x ^ 2 cm²

Now when each edge is increased by 50 %,

Measure of the edge of new cube = x + 50 % of x

Measure of the edge of new cube = x + 50x / 100

Measure of the edge of new cube = x + x / 2

Measure of the edge of new cube = ( 3x / 2 ) cm

Total surface area of the new cube = 6 * ( 3x / 2 ) ^ 2

Total surface area of the new cube = 6 * ( 9x^2 / 4 )

Total surface area of the new cube = 54x ^ 2 / 4

Total surface area of the new cube = 13.5 x ^ 2 cm²

Increase in the total surface area = 13.5 x ^ 2 - 6 x ^ 2

Increase in the total surface area = 7.5 x ^ 2 cm²

Now,

Percentage increase in the total surface area = ( Increase in total surface area * 100 ) / Initial total surface area of the cube

Percentage increase in the total surface area = ( 7.5 x ^ 2 * 100 ) / 6 x ^ 2

Percentage increase in the total surface area = 750 x ^ 2 / 6 x ^ 2

Percentage increase in the total surface area = 750 / 6

Percentage increase in the total surface area = 375 / 3

Percentage increase in the total surface area = 125 %