The mass, $M$ grams, of a cylindrical clay is directly proportional to the cube of its radius, $r$ centimetres. The mass of the cylindrical clay is increased by 700%. Calculate the percentage increase in the radius of the cylindrical clay. Answer ... %

1. Convert the percentage increase in mass to a multiplier.

A $700\%$ increase means the new mass is
$100\%+700\%=800\%$
of the original mass.

So the mass multiplier is
$\frac{800}{100}=8.$

2. Use $M \propto r^3$ to find the radius multiplier and hence the percentage increase.

Since $M \propto r^3$,
$\frac{M_2}{M_1}=\left(\frac{r_2}{r_1}\right)^3.$

Given $\frac{M_2}{M_1}=8$,
$\left(\frac{r_2}{r_1}\right)^3=8$
$\frac{r_2}{r_1}=\sqrt[3]{8}=2.$

So the new radius is $200\%$ of the original radius.

Percentage increase in radius
$=200\%-100\%=100\%.$