# Question c1052

Sep 11, 2016

#### Explanation:

Since the density is given as $\text{2.33 g/cm"^3}$, convert the mass of the cylinder from $\text{1.84 kg}$ to grams.

$1.84 \cancel{\text{kg"xx"1000 g"/cancel"1 kg"="1840 g}}$

The density formula is: $\text{density"="mass"/"volume}$

Rearrange the density formula to isolate volume.

$\text{volume"="mass"/"density}$

To determine the volume of the cylinder, divide the mass by the density.

(1840 cancel"g")/(2.33 cancel"g"/"cm"^3)="789.7 cm"^3#

The volume of the cylinder is ${\text{789.7 cm}}^{3}$.

The formula for the volume of a cylinder is: $V = \pi \cdot {r}^{2} \cdot l$, where $\pi$ is pi, $r$ is radius, and $l$ is length.

To determine the radius of the cylinder, rearrange the formula to isolate ${r}^{2}$.

${r}^{2} = \frac{V}{\pi \cdot l}$

Plug the known values into the formula.

${r}^{2} = 789.7 \text{cm"^3"/"pi*13.6 "cm}$

${r}^{2} = \text{18.48 cm"^2}$

Take the square root of both sides.

$\sqrt{{r}^{2}} = \sqrt{{\text{18.48 cm}}^{3}}$

$r = \text{4.30 cm}$ (rounded to three significant figures)