Math, asked by neerajrawat1, 1 year ago

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

Answers

Answered by GB2010
9
Hiii...


Let side of cube is a ....
New side = a + a/2 = 3a/2 ...

Area = 6a^2 ...

New Area = 6 × (3a/2 )^2 ..
= 6 × 9/4 × a^2 ..
= 54/4 a^2 ...

Percentage increse is 125 % ...
Answered by BrainlyPromoter
3

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 %

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