Question

If each edge of a cube is doubled then the percentage increase in its total surface area is

Answer 1

Answer

percentage increase in its total surface area 300%

Explanation

Surface area of a cube with side 'a' can be written as

Surface area A =6a^2

If each edge of a cube is doubled, side of cube a becomes 2a

Therefore, Surface area A =6a^2 = 6 (2a)^2 = 24a^2

then the percentage increase in its total surface area =[ (difference of surface area) x 100]/initial surface area

Difference of surface area= 24a^2 - 6a^2=18a^2

   percentage increase in its total surface area = (18a^2 x 100)/6a^2 300%

Answer 2

If each edge of a cube is doubled then the percentage increase in its total surface area is

Consider a cube. Let each edge of a cube be doubled.

surface area of a cube = 6a

side of cube is given by a

surface area of a cube will be 6a^2

side of a cube will be 2a

Surface area will be equal to 6(2a)^2 which is again equal to 24 a^2

When finding a percentage it has to be multiplied by 100

Percentage increase will be 24a^2 - 6a^2/6a^2 x 100

18a^2/6a^2 x 100 = 300%

So the percentage increase in total surface area is 300%