Question #c1052

1 Answer
Sep 11, 2016

Answer:

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)