# Math Help - surface areas and volumes

1. ## surface areas and volumes

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

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

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