Question

If each edge of a cube is increased by 50 percent what will be the percentage increase in the surface area of cube

Answer 1

Let the edge of cube be a
TSA = 6a^2

New Edge = a +50% of a
= a + 50a/100
= a + a/2
= 3a/2

TSA of new cube = 6 * (3a/2)^2
= 6*9a^2 /4
= 27a^2/2

Increase in TSA = 27a^2 /2 - 6a^2
= (27a^2 - 12a^2) / 2
= 15 a^2 /2


% of increase in TSA = (15 a^2 /2) * 100 / 6a^2
= 15a^2 *50 / 6a^2
= 15 * 50 / 6
= 5 * 25
= 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 %