1. The cylindrical container is four-fifths full of powder. Show ALL work for the following. a. The total capacity of the container in terms of π is________________________. b…

Question

asked Aug 17, 2019 149k views

1 Answer

Zhuoran He · Answer 1 · 2019-08-22T08:08:06+0000

By definition, the volume of a cylinder is given by:

$V = \pi r ^ 2h$

Where,

r: cylinder radius

h: cylinder height

Therefore, the total capacity of the container is:

$V = \pi (6) ^ 2 (18)$

Rewriting we have:

$V = 648 \pi$

Then, the amount of total dust is given by:

V '= (4)/(5) V

Where,

V: volume of the container

Substituting values:

$V '= (4)/(5) (648 \pi)$

Rewriting:

$V '= 518.4 \pi$

Answer:

The total capacity of the container in terms of π is:

$V = 648 \pi$

The volume of the powder in terms of π is:

$V '= 518.4 \pi$