Answer:
The volume of the pill is [tex]V=452\ mm^{3}[/tex]
Step-by-step explanation:
Find the volume of the pill in cubic millimeters
we know that
The volume of the pill is equal to the volume of the cylinder plus the volume of a sphere (two hemisphere is equal to one sphere)
so
we have
[tex]V=\frac{4}{3}\pi r^{3}+\pi r^{2}h[/tex]
[tex]r= (18-12)/2=3\ mm\\ h=12\ mm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(3)^{3}+(3.14)(3)^{2}(12)\\V=452\ mm^{3}[/tex]
Volume is a three-dimensional scalar quantity. The volume of the pill is 452.3893mm³.
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The height of the cylindrical portion is 12mm and the overall height is 18mm. Therefore, the radius of the hemisphere at any one end will be half the difference between the cylindrical portion and the overall height. Thus,
The radius of the sphere, R = (18mm - 12mm)/2 = 3mm
The volume of the capsule
= Volume of cylinder +2(Volume of the hemisphere)
= (πR²h) + 2[(4/6)πR³]
= (π×3²×12) + 2[(4/6)×π×3³]
= 339.292mm³ + 113.0973mm³
= 452.3893 mm³
Hence, the volume of the pill is 452.3893mm³.
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