Question

each edge of a cube is increased by 50%.find the percentage increased in the surface area?

Answer 1

hey!!

here is your answer >>>

The general formula for a surface area of a cube is 6(a)^2,

where, a is the side!

Now, the side is increased by 50%! .

then, the side will be

>>>
a + (50/100)a

a + (a/2)

3a/2!

This is the increased side,

original is 'a'!

Now, we have to find the percent increase!

The surface area of the increased edge cube is !

>>>

(6)(3a/2)^2

(6)(9a^2/4)

27a^2/2 is the surface area!

Re surface area is (6)(a)^2!

increased surface area is 27a^2/2 - 6a^2

=> 15a^2 / 2!

Increased percent is the difference/original (100)

so,

(15a^2 / 6a^2 ) (100)

=> a^2 will be cancelled!

(15/6)(100)!

(5/2)(100)

=> 250% increase is the answer!

Hope my answer 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 %