The question is incomplete. Below is the complete question:
A pill has the shape of a cylinder with a hemisphere at each end. The height of the cylindrical portion 11
mm and the overall height is 18 mm.
(a) Find the volume of the pill in cubic millimeters. Round to the nearest cubic
millimeter.
(b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per
cubic millimeter? Round to the nearest tenth of a cubic millimeter.
Answer:
a. 603 cubic millimetre
b. 1.7 mg/mm^3
Step-by-step explanation:
The since the pill has the shape of a cylinder and 2 hemispheres at both ends of the cylinder, if we are to calculate the volume, we will need the formula for calculating the volume of a cylinder and the volume of a hemisphere:
a. The volume of a cylinder = π×r^2×h and the volume of a hemisphere = 2×π×r^3.
The total height of the pill is 18mm but that of the cylinder specifically is 11cm, so 18 - 11 = 7mm.
This becomes the combined radius of the two hemispheres. We will now split it into 2:
7/2 = 3.5mm
This becomes the radius of each of the 2 hemispheres and will be used for calculating their respective volumes. The cylinder too will share same radius with the spheres (3.5mm). Let us take π as 3.14
Volume of the pill is then:
V =[2× (2/3 × π×r^3)] + π×r^2×h
V = [2×[(2/3) × 3.14 × 3.5^3]] + 3.14 × (3.5^2) × 11
[2 × (89.752)] + 423.115
179.504 + 423.115
= 602.619
= 603mm^3 (nearest cubic millimetre)
b. In order to find out how much vitamin C the pill will contain per cubic millimetre if it is to contain 1000mg of vitamin C, we will simply divide 1,000mg by the already calculated volume:
= 1000/63
= 1.658
= 1.7 mg/mm^3 (nearest tenth)
is the sample proportion.