# surface areas and volumes

• Nov 23rd 2006, 12:40 AM
anjana
surface areas and volumes
how much will the volume of sphere be reduced if radius of sphere is halfed?:confused:
• Nov 23rd 2006, 12:59 AM
earboth
Quote:

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

Hello, Anjana,

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

Then you have $V_1=\frac{4}{3} \pi r^3$ and
$V_2=\frac{4}{3} \pi (\frac{1}{2}r)^3$ . Expand:
$V_2=\frac{4}{3} \pi \frac{1}{8}r^3=\frac{1}{8} \cdot \frac{4}{3} \pi r^3$

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

EB
• Nov 23rd 2006, 03:26 AM
CaptainBlack
Quote:

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

As a rule the volume of similar solids scales as the cube of corresponding
linear dimensions, so halving the radius scales the volume by (0.5)^3.

RonL