Question

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. The volume of the powder in terms of π is _______________________.

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 '= (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`