Question

A cylinder has a height of `4` feet and a diameter of `12` inches. What is the volume of the cylinder?

Answer 1

Before calculating the volume of this cylinder, we must either convert the diameter to feet or the height to inches. I'll do the latter, to avoid getting a very small number.

Recall that there are `12` inches in `1` foot. Thus, we can state:

`(12" in.")/(1" ft.") =(x)/(4" ft."`

`x = (12" in." xx 4cancel" ft.")/(1cancel"(ft.)")`

`x = 48" in."`

Hence, the cylinder has a height of `48` inches.

Now, we can apply the formula for volume of a cylinder to effectuate our calculation. The formula in question is `V = a_"base" xx h`, or `V = r^2pi xx h`.

However, we know our diameter but we don't know our radius. As you probably know, the diameter is linked to the radius b the formula `d = 2r`. Solving for `r` and substituting:

`r = d/2`

`r = 12/2`

`r = 6`

`:.` The radius of the cylinder measures `6` inches.

`V = r^2pi xx h`

`V = 6^2pi xx 48`

`V = (36 xx 48)pi`

`V = 1728pi" in"^2`

Note that this answer is in exact value. Rounded to two decimal places, the volume is `5428.67" in"^2`.

Practice exercises:

1. Determine the volume of a cylinder whose base has a circumference of `18pi" yd."` and whose height measures `27" ft."`.

Note:

•The formula for circumference of a circle is `C = dpi`, where `C` is the circumference.

•There are `3` feet in a yard.

Challenge Problem:

The volume of an industrial sized water cistern is `200pi" ft"^2`. The height measures `3` feet more than the radius. Determine algebraically the circumference of the base of the cistern, using the formula given above.

Hopefully this helps, and good luck!