Question

0. A pill has the shape of a cylinder with a hemisphere at each end. The height of the cylindrical portion 11

Answer 1

Answer:

Part a) The volume of the pill is $603\ mm^{3}$

Part b) $1.7\frac{mg}{mm^{3}}$

Part c) $215\ mg$

Step-by-step explanation:

Part a) 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

$V=\frac{4}{3}\pi r^{3} +\pi r^{2}h$

we have

$r= (18-11)/2=3.5\ mm$

$h=11\ mm$

assume

$\pi =3.14$

substitute

$V=\frac{4}{3}(3.14)(3.5)^{3} +(3.14)(3.5)^{2}(11)$

$V=603\ mm^{3}$

Part 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?

Divide 1,000 milligrams by the volume

$1,000/603=1.7\frac{mg}{mm^{3}}$

Part c) Another pill that is entirely spherical has a diameter of 10 millimeters and contains 1.5 milligrams of  vitamin C per cubic millimeter. How much less vitamin C does this second pill contain, rounded to the

nearest milligram, than the one pictured?​

step 1

Find the volume of the sphere

The volume of the sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

we have

$r=10/2=5\ mm$ ----> the radius is half the diameter

assume

$\pi =3.14$

substitute

$V=\frac{4}{3}(3.14)(5)^{3}$

$V=523.33\ mm^{3}$

step 2

Multiply the volume by 1.5 milligrams of  vitamin C per cubic millimeter

so

$523.33*1.5=785\ mg$

step 3

Find the difference

$1,000-785=215\ mg$