Question

If eight cubes are stacked to form a big cube, then find the percentage decrease in the total surface area

• A. $30\%$
• B. $40\%$
• C. $50\%$
• D. $60\%$

Answer 1

Answer: (C)

$50\%$

Total surface area of a cube of side $a=6a^2$
So, total surface area of $8$ cubes $=8\times 6a^2=48a^2$
When eight such cubes are stacked, the resulting figure will be a cube of
length $=2a$
breadth $=2a$
height $=2a$
And total surface area of the cube of side $2a=6{\left(2a\right)}^2=24a^2$
So, $\%$ decrease in total surface area $=\frac{48a^2-24a^2}{48a^2}\times 100=50$ $\%$.