Question

if the radius of a sphere is half is volume becomes how many times a volume of original sphere

Answer 1

Dear student
$$\begin{gathered} TheradiusofthesphereisRcm \\ Thusthevolumeofthespherewillbe\frac{4}{3}{\mathrm{\pi R}}^3 \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{question}: \\ \mathrm{The}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{sphere}\mathrm{is}\mathrm{halved},\mathrm{therefore},\mathrm{the}\mathrm{rdaius}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{sphere}=\frac{\mathrm{R}}{2}\mathrm{cm} \\ \mathrm{Thus},\mathrm{the}\mathrm{new}\mathrm{volume}\mathrm{of}\mathrm{sphere}\mathrm{will}\mathrm{be}\frac{4}{3}\mathrm{\pi }{\left(\frac{\mathrm{R}}{2}\right)}^3 \\ \mathrm{The}\mathrm{ratio}\mathrm{of}\mathrm{volumes}\mathrm{will}\mathrm{be}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{Actual}\mathrm{sphere}}{\mathrm{Voluem}\mathrm{of}\mathrm{New}\mathrm{sphere}}=\frac{\frac{4}{3}{\mathrm{\pi R}}^3}{\frac{4}{3}\mathrm{\pi }{\left(\frac{\mathrm{R}}{2}\right)}^3}=\frac{8}{1} \\ \Rightarrow \mathrm{The}\mathrm{ratio}\mathrm{will}\mathrm{be}8:1 \end{gathered}$$
So, the volume of the actual sphere is 8 times the value of the new sphere.
Regards