The correct answer is:
[C]: "
37, 680 mm³ " .
________________________________________________________
Explanation:
________________________________________________________
The formula for the volume, "
V" , o
f a cylinder is: → V = 
* 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 " .
________________________________________________________ → 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, t
he formula for the volume, "
V"
, of a cylinder is:______________________________________________________ → Volume = (Base area) * (height) ;
= ( r² ) * h ;
______________________________________________________
→ V = r² h ;
in which: "
V = volume {in "
cubic units" ; or, write as "
units³ "
} ;
"
r = radius length" ;
"
h = height" ;
_____________________________________________________ → Now,
we shall solve for the volume, "
V", of the given cylinder in this question/problem:
_____________________________________________________ → V = 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
; 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 " ;
→ so we shall use this
"numerical value" as an "
approximation" ;
_______________________________________________________Now, let us plug in our known values into the formula;
and calculate
to find the volume, "
V",
of our given cylinder;
as follows:_______________________________________________________
→ V = 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
__________________________________________________
The volume is: "
37, 680 mm³ " ;
→ which is:
Answer choice [C]: "
37, 680 mm³ " .
___________________________________________________
Hope this answer and explanation—albeit lengthy—is of some help to you.
Best wishes!
