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 . ___________________________________________________
