Question

The surface area of a solid sphere is increased by $21$% without changing its shape.Find the percentage increase in its :
(i)radius
(ii)volume

Answer 1

Previous surface area $=x$

then new surface are $=1.21x$

Now surface Area $\propto (radius{)}^2$

then $\frac{x}{1.21x}={\left(\frac{r_{old}}{r_{new}}\right)}^2$

$r_{new}=1.1r_{old}$

$10\%$ increase . in radius

Now volume $\propto (radius{)}^3$

then volume $\propto (surfacearea{)}^{3/2}$

$\frac{v_{old}}{V_{new}}={\left(\frac{x}{1.21x}\right)}^{3/2}$

$V_{new}=1.331V_{old}$

$33.1\%$increase in volume