Question

Small grey identical cubes are removed from all faces of a cube as shown in the figure. By what percentage will the surface area of the cubeincrease?

• A. 22.22%
• B. No change
• C. 30.77%
• D. 44.44%

Answer 1

The correct option is D 44.44%

If one small grey cube is removed, surface area of the cube gets decreased by area of two squares (the outer faces of the grey cube).
Once a cube is removed, the remaining 4 surfaces are exposed which now form a part of the total surface area of the big cube.
Therefore, net change in the surface area due to removal of one grey cube = area of (-2+4) square faces = +2 square faces.
Now,
12 grey cubes are removed in total.
$\therefore$ Increase in the surface area = 12 $\times$ area of 2 square faces
= area of 24 square faces
Side of each grey cube = $\frac{6}{3}$ = 2 m
$\therefore$ Increase in the surface area = $24\times 2^2$ = $96m^2$

Initial surface area of the cube = $6a^2$ = $6\times 6^2$ = $216m^2$

Percentage increase in surface area = $\frac{Increaseinsurfacearea}{Initialsurfacearea}\times 100$
= $\frac{96}{216}\times 100$
= $44.44$%