How do you find the density of a cone of radius #"5 cm"# and height #"2 cm"# if its mass is equal to #"6 g"# and its volume is equal to #"52.36 cm"^3# ?

1 Answer
Sep 6, 2017

Answer:

Here's what I got.

Explanation:

Start by calculating the volume of the cone.

http://www.onlinemathlearning.com/volume-cone.html

In your case, you have

  • #r = "5 cm" -># the radius of the cone
  • #h = "2 cm" -># the height of the cone

Plug your values into the equation to get

#V = 1/3 * pi * "5 cm"^2 * "2 cm"#

#V = "52.36 cm"^3#

Now, to find the density of the material, you must determine the mass of exactly #"1 cm"^3# of material. To do that, use the fact that #"52.36 cm"^3# of material have a mass of #"6 g"#

#1 color(red)(cancel(color(black)("cm"^3))) * "6 g"/(52.36 color(red)(cancel(color(black)("cm"^3)))) = "0.1146 g"#

Since this represents the mass of exactly #"1 cm"^3# of this material, you can say that

#color(darkgreen)(ul(color(black)("density = 0.1 g cm"^(-3)))#

The answer is rounded to one significant figure.

SIDE NOTE This is a very low value for the density of a material, so make sure to double-check the values given to you for the mass of the cone and for its dimensions.