Q. 434.1( 16 Votes )

If each edge of a cube is increased by 50%, the percentage increase in the surface area is
A. 50%

B. 75%

C. 100%

D. 125%

Answer :

Given: Edge of a cube is increased by 50%


Let ‘a’ be the Edge of the cube


Area of the cube is : 6l2 (where ‘l’ is the edge of a cube)


Let A1 be the initial surface area of the cube.


A1 = 6a2


Now,


50% of the edge is: a × =


Edge = a + after increasing edge by 50%


That is edge of the cube after increasing it by 50% is


Let A2 be the surface area of the cube after increasing the edge by 50%


A2= 6 × ()2 = × 6a2


Here increase in area = A2 –A1


increase in area = × 6a2 – 6a2 = × 6a2


Now, increase in percentage is:


Increase in % = × 100 = × 100 = 125%


If each edge of a cube is increased by 50%, then the percentage increase in the surface area is 125%

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