StartLayout 1st row StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot space c greater-than
-or-equal-to 0 and d greater-than-or-equal-to 0. 2nd row = StartRoot StartFraction 25 times 10 c squared times c Over 9 d Superscript 6 Baseline EndFraction EndRoot. 3rd Row = StartFraction StartRoot 25 EndRoot times StartRoot c squared EndRoot times StartRoot 10 c EndRoot Over StartRoot 9 d Superscript 6 Baseline EndRoot EndFraction EndLayout
Based on the work shown on the left, what is the simplest form of StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot ?
Based on the work shown on the left, what is the simplest form of StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot ?
1 answer:
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All real numbers.
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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 =
* 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, the 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!
________________________________________________________
Explanation:
________________________________________________________
The formula for the volume, "V" , of a cylinder is:
→ V =
→ 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, the formula for the volume, "V" , of a cylinder is:
______________________________________________________
→ Volume = (Base area) * (height) ;
= (
______________________________________________________
→ V =
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 =
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
→ 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 =
= (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!
