Question

If each side of a cube is increasesd by 40%, then
the percentage increase in its surface area is
(A) 100%
(B) 88%
(C) 96%
(D) 99%​

Answer 1

Hello!

Answer

96%

Step by step explanation

There are two ways to solve this question.

Approach 1 : Final and Initial value.

Let the edge of the cube be equal to ‘a’ units.

Thus, the initial surface area (A1) = a² units²

Now, the edge of the cube increases by 40% OR the new edge length = a + 40% of a = 1.4a.

Thus, the final surface area (A2) = (1.4a)² = 1.96a² units²

Percentage change = [(A2 - A1)/(A1)] x 100 = [(1.96a² - a²)/(a²)] x 100

= 0.96 x 100

= 96%.

Approach 2 : Chain rule formula.

If the edge of the cube increases by a% , the percentage change in the area = a + a + (a²)/100.

Here, a = 40.

So percentage change in the area = 40 + 40 + (40²)/100 = 96%

Hope this helps! :)