Dimensions of a cubical shape room are increased by 10%. What increase will be there in its floor area?

Correct option is C

Given:

A cubical-shaped room has all its dimensions increased by 10%.

Find the increase in its floor area.

Formula Used:

If each side increases by x%, then

% increase in area = $$\left(1+\frac{x}{100}\right)^2 - 1$$​​

Solution:

Let original side of the cube = a

Original floor area = a²

New side = a + 10%  of  a = 1.1a

New floor area = 1.1a² = 1.21a²

Increase in floor area:

​$$1.21a^2 - a^2 = 0.21a^2$$​​

%increase = 21%

Alternate Solution (Exam Trick):

Area depends on square of dimensions →

Increase = 10 + 10 +$$\frac{10×10}{100}$$​ = 20% + 1% = 21%