Question

If each edge of a cube is doubled, How many times will it's surface area increase? and How many times will its volume increase?

• A. $4$ times ; $8$ times
• B. $4$ times ; $4$ times
• C. $8$ times ; $8$ times
• D. None of these

Answer 1

The correct option is A $4$ times ; $8$ times

Surface area of a cube $=6l^2$
If l is doubled $=6{\left(2l\right)}^2=6\times 4\times l^2=4\left(6l^2\right)$
Surface area increase of a cube $=l^3$
If l is doubled , volume $={\left(2l\right)}^3=2^3{l}^3=8{\left(l\right)}^3$
Volume increase by $8$ times