Question #c1052

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Answer 1 · 2016-09-11T20:17:18

The radius is 4.30 cm.

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)