Question

0. 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.
(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?​

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

$1,000-785=215\ mg$