Question

If each edge of a cube is increased by 50 percent.Find the percentage increase in the surface area of the cube .

Answer 1

Hi friend
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Your answer
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Percentage by which each side of the cube is increased = 50%

Now,
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Let the measure of the sides initially be a.

Then,
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Initial surface area = 6a²

New side = a + 50a/100 = a + a/2 = 3a/2

New surface area = 6 × (3a/2)² = 6 × 9a²/4 = 54a²/4

Percentage increase of the surface area if the cube

$= > ( \frac{ \frac{54a {}^{2} }{4} }{6a {}^{2} } \times 100)\% \\ \\ = > 75\%$
Therefore ,
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The percentage increase in surface area is 75%.

HOPE IT HELPS

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 %