If each side of a cube is decreased by 12%, then the percentage decrease in its surface area is:

Correct option is C

Given: ​

Each side of a cube is decreased by 12%

Formula Used:

Surface area of cube = 6a²

Solution:

Decrease in side = 12% = 12/100 = 3/25

Let Original side length = 25 unit

So, new side length = 25 - 3 = 22 

Original Surface area = $$6 × 25^2 = 3750$$​​

New Surface area = 6 × $$22^2$$​ = 2904

Decrease in surface area = $$\frac{3750 - 2904}{3750} = \frac{846}{3750}$$​ × 100 = 22.56% 

Alternate Solution:​

As we know surface are has two variable x and y 

here each side decreased by 12% 

means x = -12% and y = -12% 

Now, successive percentage;

= -12 -12 +$$\frac{(-12)(-12)}{100}$$ 

= -24 + 1.44 

= -22.56%(decrease)