Question

LAST QUESTION! Please help! Please

Answer 1

The correct answer is:  [C]:  " 37, 680 mm³ " .
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Explanation:
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The formula for the volume, "V" , of a cylinder is:

                →   V  =   $\pi$  *  r²  *  h  ;  

                           → in which "r = length of radius" ;  "h = height" ;             ________________________________________________________

     {Note that the formula for the volume, "V" , of a cylinder is:
     
                              →   " Base area * height " .
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         →  Specifically, for a cylinder, the "Base area" is the area of a "circle", because the base is a circle;  

          →  and the formula for the "area of a circle = [tex] \pi [/tex] * r² " ;

          →  in which "r = length of the radius" . 

As such, the formula for the volume, "V" ,  of a cylinder is:
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       →   Volume  =  (Base area) * (height) ; 

                             =  ( $\pi$ r² ) * h  ;
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       →   V  =  $\pi$  r²  h  ; 

                 in which:  "V = volume  {in "cubic units" ;  or, write as " units³ " } ;

                                  "r = radius length" ; 

                                  "h = height" ;
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  →  Now, we shall solve for the volume, "V", of the given cylinder in this question/problem:
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          →   V  = $\pi$  r²  h  ; 

                      in which: "r = radius = ? "  ; 

                        →  To find "r" ;  We are given the diameter, "d = 40 mm" ; 
 
                        →  Note that:  "r = d/2 = (40 mm) / 2 = 20 mm " ; 

                              {i.e., "the radius is half of the diameter".}.  

                        →  " r = 20 mm " ;  

                        →  " h = height = 30 mm " {given in figure) ; 
      
                        →  For $\pi$ ; let us use " 3.14 " — which is a commonly used approximation.  

             →  For this question/problem, none of the answer choices are given "in terms of $\pi$ " ;
     →   so we shall use this "numerical value" as an "approximation" ; 
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Now, let us plug in our known values into the formula;
     and calculate to find the volume, "V", of our given cylinder; as follows:
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    →    V  = $\pi$  r²  h  ; 

                =  (3.14) * (20 mm)²  * (30 mm) ; 

                =  (3.14) * (20)² *  (mm)²  * (30 mm) ;
          
                =  (3.14) * (20)² * (30) * (mm³) ;

                =  (3.14) * (400) * (30) * (mm³) ; 

                =  37, 680 mm³
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The volume is:  " 37, 680 mm³  " ;  

          →  which is:  Answer choice  [C]:  " 37, 680 mm³ " .
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Hope this answer and explanation—albeit lengthy—is of some help to you.
Best wishes!