What is the Percentage Increase in the Total Surface Area? if

Answer: (2) 56.25 %

Explanation:-
Let the edge of a surface area = a

Formula-
The surface area of a cube = 6a²
Where, a = edge of a cube.
Then, the surface area of a cube = 6a²

If edge increased by 25 %,

Then , the surface area of a cube = 6 (a + a 25/100)²
= 6 (a + a/4)²
= 6 (5a/4)²
= 6 x 5 a x 5 a /4 x 4
= 75 a²/8
Increased surface area = 75 a²/8 – 6 a²
= (75 a² – 48 a²)/8
= 27 a²/8
Percentage of increased area = 27 a² x 100/8 x 6 a²
= 9 x 25/2 x 2
= 225/4
= 56.25 %
Then, the increased surface area is 56.25 %.

Hence, the answer answer is (2) 56.25%.