Question

Find percentage change in the surface area and volume of a cube when side is doubled.

Answer 1

Let’s take side length of cube be x cm.
Now, total surface area =$6x^2$ $(\because 6x(side{)}^2)$
$Volume=(side{)}^3=x^3$
Now, side scaled by factor 2
So, side length of nee cube = (2x)
Total surface area = $6(2x{)}^2=24x^2$
Volume = $(2x{)}^3=8x^3$
$\therefore$ scaled factor o surface area = $\frac{24x^2-6x^2}{6x^2}$
$=\frac{18x^2}{6x^2}\times 100\%=300\%$
Volume =$\frac{8x^3-x^3}{x^3}=\frac{7x^3}{x^3}\times 100\%$
$=700\%$