Question

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

Answer 1

Let the edge of cube be a

Surface Area = 6a^2

Edge of cube after increase = a + 50% of a

= a + a/2

= 3a/2

Surface Area of new cube = 6 × ( 3a/2)^2

= 6 × ( 9a^2 / 4)

= 54a^2 / 4

Increase in Surface Area = 54a^2 / 4 - 6a^2

= ( 30a^2 / 4)

= 15a^2 / 2

Increase in Percentage = ( 15 a^2 / 2 × 100) / 6a^2

= 750 / 6

= 125 %

Answer 2

Explanation:

Let the edge = a cm   

So increase by 50 % = a + a/2 = 3a/2  

Total surface Area of original cube = 6a^2  

TSA of new cube = 6(3a2)^2 =6(9a24)=  13.5a^2   

Increase in area = 13.5a^2-6a^2 =7.5a^2  

 7.5a2 Increase % =7.5a26a^2×100 = 125%

Hope its help!!!!