Q:

What is the volume of a sphere with a radius of 7mm

Accepted Solution

A:
1)  The answer, in terms of  "π", is:
_________________________________
  "  ([tex] \frac{1372 mm^3}{3} [/tex]) *  π    mm³ " .
___________________________________________________
2) The answer, using "3.14" for "π", is:
___________________________________________________
" 1436.0266666666666667  mm³ " ; round to: " 1436.027 mm³ " ; 

        or; write as: " 1436 [tex] \frac{2}{75} [/tex]  mm³ " .
___________________________________________________
Explanation: 
____________________________________________
The formula for the volume, "V" of a sphere is:

V = [tex] \frac{4}{3} [/tex] * π* r³ ;

in which "r" = radius = "7 mm" {given}.

We can solve using "3.14" for "π" ; or we can solve in terms of "π" ;
_________________________________________
1)  In terms of "π" :
_________________________________________
   V = [tex] \frac{4}{3} [/tex] * π * r³ ;

      = [tex] \frac{4}{3} [/tex] * π * (7 mm)³ ;

      = [tex] \frac{4}{3} [/tex] * π * (7 * 7 * 7 * mm³) ;
 
      = [tex] \frac{4}{3} [/tex] * π * (49 * 7 * mm³) ;

      = [tex] \frac{4}{3} [/tex] * π * (343 mm³) ;

      = [tex] \frac{4* 343 mm^3}{3} [/tex]) * π   mm³

      =  ([tex] \frac{1372 mm^3}{3} [/tex]) *  π    mm³  ;

________________________________________________________
2)  Using "3.14" for "π" :
________________________________________________________
     V = [tex] \frac{4}{3} [/tex] * π * r³ ; 

        = [tex] \frac{4}{3} [/tex] * (3.14)* (7 mm)³ ;

        = [tex] \frac{4}{3} [/tex] * (3.14) * (7 * 7 * 7 * mm³) ;

        = [tex] \frac{4}{3} [/tex] * (3.14) * (49 * 7 * mm³) ;

        = [tex] \frac{4}{3} [/tex] * (3.14) * (49 * 7 * mm³) ;

        = [tex] \frac{4}{3} [/tex] * (3.14)  * (343 mm³) ;

        = { [tex] \frac{4}{3} [/tex] }  * (3.14 * 343 mm³) ;

        = { [tex] \frac{4}{3} [/tex] } *  (1077.02 mm³) ;

        = (4 * 1077.02 mm³) / 3 ; 

        = (4308.08 mm³) / 3 ; 
__________________________________________________________
        =  1436.0266666666666667  mm³ ;  round to: " 1436.027 mm³ " ;

        or; write as: " 1436 [tex] \frac{2}{75} [/tex]  mm³ " .
__________________________________________________________