Question

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

Answer 1

Answer:

Let the original side be a then

Original surface area S=6a

2

When side is increased by 50%, side becomes

2

3

a then

Surface area s=

2

27

a

2

Hence,

Surface area is increases by x=

6a

2

2

27

a

2

−6a

2

×100=125%

This is the required solution

Answer 2

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Solution:

Let x be the edge of a cube.

Surface area of the cube having edge x = 6x2 ………..(1)

As given, a new edge after increasing the existing edge by 50%,

we get The new edge = x + 50 x /100The new edge = 3x/2

Surface area of the cube having edge 3x/2 = 6 x (3x/2)2=(27/2)x2……..(2)

Subtract equation (1) from (2) to find the increase in the Surface Area:

Increase in the Surface Area = (27/2)x2 – 6x2

Increase in the Surface Area = (15/2)x2

Now,Percentage increase in the surface area = ((15/2)x2 / 6x2) x 100

= 15/12 x 100

= 125%

Answer: 125