A drug manufacturing company wants to manufacture a capsule that contains a spherical pill inside. The diameter of the pill is 4mm and the capsule is cylindrical, with hemispheres on either end. The length of the capsule between the two hemispheres is 10mm. Describe how we could find the exact volume the capsule will hold, excluding the volume of the pill.
2007-02-02 03:29:42 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Other - Science
Though you give the size of the pill, you give no sizing for the capsule, unless you're saying that the pill fits EXACTLY within the diameter of the capsule, thus making the insides 4mm across.
Thus, the 4mm sphere volume has to be first.
The formula for this is 4/3 x pi x r cubed.
This gives us the volume of the pill at 33.5104 Cubic MM.
The ends of the capsule if cut off from the rest would form a single sphere which would exactly match the sphere. and thus hold 33.5104 Cubic MM
The rest of the capsule is a cylinder.
The formula for this is pi x r squared x height.
Thus the volume of the cylinder is 125.664 Cubic MM
- THIS is the answer. The total volume excluding the volume of the pill, as shown above.
To figure this completely
Total volume would the the total of the spherical ends plus the cylindrical center. 33.5104 + 125.664 = 159.1744 Cubic MM and to exclude the volume of the pill
159.1744 - 33.5104 = 125.664 Cubic MM
2007-02-02 03:38:02 · answer #1 · answered by Marvinator 7 · 1⤊ 0⤋
We can assume that spherical pill is the same size that the two hemispheres of the capsule put together, so we have to deduct
4 mm to the total length of the capsule:
10mm - 4 mm = 6 mm
This would be the height of the cylinder (without hemispheres) and its diameter would be 4 mm.
Hence the volume of the capsule is the sum of cylinder plus spherical pill:
V = V cylinder + V spherical pill
V = Pi*D²*H / 4 + (1/6)*Pi*D³
V = Pi [D²*H / 4 + (1/6)*D³]
where: Pi= 3.141592
D = diameter of the spherical pill
H = height of the cylinder (discounting the hemispheres)
Substituting values, we get:
V = 108.9 mm³
That's it!
Good luck!
2007-02-02 03:51:30 · answer #2 · answered by CHESSLARUS 7 · 0⤊ 0⤋
Find the volume of the pill.
Find the volume of the capsule.
Subtract.
By the way, what is the thickness of the capsule walls?
2007-02-02 03:50:11 · answer #3 · answered by morningfoxnorth 6 · 0⤊ 0⤋