Question

1. The cylindrical container is four-fifths full of powder. Show ALL work for the following.

Answer 1

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:

$V '= \frac{4}{5} V$

Where,

V: volume of the container

Substituting values:

$V '= \frac{4}{5} (648 \pi)$

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:

$V '= 518.4 \pi$