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 = [tex] \pi [/tex] * 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) ;
= ( [tex] \pi [/tex] r² ) * h ;
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→ V = [tex] \pi [/tex] 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 = [tex] \pi [/tex] 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 [tex] \pi [/tex] ; 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 [tex] \pi [/tex] " ;
→ 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 = [tex] \pi [/tex] 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!
