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hoa [83]
3 years ago
5

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

Mathematics
2 answers:
sammy [17]3 years ago
5 0

Answer:

3.91

Step-by-step explanation:

Triss [41]3 years ago
4 0
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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Complete question:

Dr. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?

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Step-by-step explanation:

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