The volume of new medicine capsule is 339.12 cubic millimeters, if the cylinder portion of the capsule is 8 millimeters long and has a diameter of 6 millimeters.
Step-by-step explanation:
The given is,
Capsule shaped like a cylinder with a half sphere at each end
The cylinder portion of the capsule is 8 millimeters long
A diameter of 6 millimeters
[tex]\pi[/tex] = 3.14
Step:1
Volume of new medicine capsule = Volume of cylinder +
2( Volume of half sphere ).....(1)
Step:2
Formula for Volume of cylinder,
[tex]V_{cylinder} = Bh[/tex]......................(2)
Where, B - Base area of cylinder
h - Height of cylinder
Base area, [tex]B=\pi r^{2}[/tex]
Radius of cylinder, r = 3 millimeters ( [tex]r= \frac{d}{2} = \frac{6}{2} = 3[/tex] )
B = [tex]\pi[/tex] × [tex]3^{2}[/tex]
= 3.14 × 9
B = 28.26 square millimeters
Equation (2) becomes,
[tex]V_{cylinder}[/tex] = ( 28.26 × 8 )
= 226.08
[tex]V_{cylinder}[/tex] = 226.08 cubic millimeters
Step:3
Formula for volume of half sphere,
[tex]V_{Half sphere} = \frac{2}{3} \pi r^{3}[/tex]..........................(3)
Where, r - Radius of sphere
From given, r = 3 millimeters ( [tex]r= \frac{d}{2} = \frac{6}{2} = 3[/tex] )
Equation (3) becomes,
[tex]V_{Half sphere} = \frac{2}{3} \pi 3^{3}[/tex]
= ( 0.666667 × 3.14 × 27 )
= 56.52 cubic millimeters
Capsule have half sphere at each end so the volume of half sphere is multiplied by 2.
= 2 × Volume of half sphere
= 2 × 56.52
= 113.04 cubic millimeters
Step:4
Volume of new medicine capsule = 226.08 + 113.04
= 339.12 cubic millimeters
Result:
The volume of new medicine capsule is 339.12 cubic millimeters, if the cylinder portion of the capsule is 8 millimeters long and has a diameter of 6 millimeters.
Answer:
The volume of new medicine capsule is 339.12 cubic millimeters
Step-by-step explanation:
EDG 2020
