Question

Question #c1052

Answer 1

The radius is 4.30 cm.

Explanation:

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

`1.84cancel"kg"xx"1000 g"/cancel"1 kg"="1840 g"`

The density formula is: `"density"="mass"/"volume"`

Rearrange the density formula to isolate volume.

`"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 `"789.7 cm"^3`.

The formula for the volume of a cylinder is: `V=pi*r^2*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=V/(pi*l)`

Plug the known values into the formula.

`r^2=789.7 "cm"^3"/"pi*13.6 "cm"`

`r^2="18.48 cm"^2"`

Take the square root of both sides.

`sqrt(r^2)=sqrt("18.48 cm"^3)`

`r="4.30 cm"` (rounded to three significant figures)