The edge of a cube is increased by 20%. What is the percentage increase in its surface area?
SA of a cube =6a^3, a=edge.
If a = 1, the SA =6
If a =1.2, the SA =6*1.2^3 =10.368
10.368 / 6 =1.728 - 1 x 100 =72.8% increase in SA of the cube.
A cube has 6 faces of equal sizes. Each side has area a2, where a is the length of an edge.
Therefore the total surface area of the cube is 6a2.
After increasing the edge length by 20%, the edge is now of length 1.2a.
The new total surface area is 6(1.2a)2, which is (1.2)2 = 1.44 times greater than the original.
Therefore the total surface area is increased by (1.44 - 1) = 44%.