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 " .
__________________________________________________________
