how much will the volume of sphere be reduced if radius of sphere is halfed?:confused:

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- Nov 23rd 2006, 12:40 AManjanasurface areas and volumes
how much will the volume of sphere be reduced if radius of sphere is halfed?:confused:

- Nov 23rd 2006, 12:59 AMearboth
Hello, Anjana,

let $\displaystyle r_1=r$ and $\displaystyle r_2=\frac{1}{2}r$

Then you have $\displaystyle V_1=\frac{4}{3} \pi r^3$ and

$\displaystyle V_2=\frac{4}{3} \pi (\frac{1}{2}r)^3$ . Expand:

$\displaystyle V_2=\frac{4}{3} \pi \frac{1}{8}r^3=\frac{1}{8} \cdot \frac{4}{3} \pi r^3$

Now compare $\displaystyle V_1\ \text{and} \ V_2$

EB - Nov 23rd 2006, 03:26 AMCaptainBlack