Respuesta :
The answer is: 3.91 inches .
___________________________________________
Note: Volume of cylinder: V = (base area) * (height);
in which: V = volume = 384 in.³ ;
h = height = 8 in. ;
Base area = area of the base (that is; "circle") = π r² ;
in which; "r" = radius;
___________________________________________
Solve for "r" :
___________________________________________
V = π r² * (8 in.) ;
384 in.³ = (8 in.) * (π r²) ;
___________________________________________
Divide EACH SIDE of the equation by "8" ;
___________________________________________
(384 in.³) / 8 = [ (8 in.) * (π r²) in.] / 8 ;
___________________________________________
to get:
___________________________________________
48 in.³ = (π r²) in.² * in. ;
___________________________________________
↔ (π r²) in.² * in. = 48 in.³ ;
___________________________________________
Rewrite this equation; using "3.14" as an approximation for: π ;
__________________________________________________
(3.14 * r²) in.² * in. = 48 in.³
_______________________________________
Divide EACH SIDE of the equation by:
"[(3.14)*(in.²)*(in.)]" ; to isolate "r² " on one side of the equation;
(since we want to solve for "r") ;
_____________________________________________________
→ [(3.14 * r²) in.² * in.] / [(3.14)*(in.²)*(in.)] = 48 in.³ / [(3.14)*(in.²)*(in.)] ;
__________________________________________________
→ to get: r² = 48/3.14 ;
________________________
→ r² = 15.2866242038216561 ;
_______________________________________
To solve for "r" (the radius; take the "positive square root" of EACH side of the equation:
__________________________________________________
→ +√(r²) = +√(15.2866242038216561)
__________________________________________________
→ r = 3.9098112747064475286 ; round to 3.91 inches .
___________________________________________________
___________________________________________
Note: Volume of cylinder: V = (base area) * (height);
in which: V = volume = 384 in.³ ;
h = height = 8 in. ;
Base area = area of the base (that is; "circle") = π r² ;
in which; "r" = radius;
___________________________________________
Solve for "r" :
___________________________________________
V = π r² * (8 in.) ;
384 in.³ = (8 in.) * (π r²) ;
___________________________________________
Divide EACH SIDE of the equation by "8" ;
___________________________________________
(384 in.³) / 8 = [ (8 in.) * (π r²) in.] / 8 ;
___________________________________________
to get:
___________________________________________
48 in.³ = (π r²) in.² * in. ;
___________________________________________
↔ (π r²) in.² * in. = 48 in.³ ;
___________________________________________
Rewrite this equation; using "3.14" as an approximation for: π ;
__________________________________________________
(3.14 * r²) in.² * in. = 48 in.³
_______________________________________
Divide EACH SIDE of the equation by:
"[(3.14)*(in.²)*(in.)]" ; to isolate "r² " on one side of the equation;
(since we want to solve for "r") ;
_____________________________________________________
→ [(3.14 * r²) in.² * in.] / [(3.14)*(in.²)*(in.)] = 48 in.³ / [(3.14)*(in.²)*(in.)] ;
__________________________________________________
→ to get: r² = 48/3.14 ;
________________________
→ r² = 15.2866242038216561 ;
_______________________________________
To solve for "r" (the radius; take the "positive square root" of EACH side of the equation:
__________________________________________________
→ +√(r²) = +√(15.2866242038216561)
__________________________________________________
→ r = 3.9098112747064475286 ; round to 3.91 inches .
___________________________________________________
