Acylinder has a volume of 384 cubic inches and a height of 8 inches, what is the radius

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 .

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Step-by-step explanation: