How do you find the density of a cone of radius "5 cm"5 cm and height "2 cm"2 cm if its mass is equal to "6 g"6 g and its volume is equal to "52.36 cm"^352.36 cm3 ?

1 Answer
Stefan V.
Sep 6, 2017

Here's what I got.

Explanation:

Start by calculating the volume of the cone.

![http://www.onlinemathlearning.com/http://volume-cone.html](https://useruploads.socratic.org/Rd6gpkWJQzVqBIMUOOuy_xvolume-of-cone.png.pagespeed.ic.2-YhHAnIvd.png)

In your case, you have

  • r = "5 cm" ->r=5 cm→ the radius of the cone
  • h = "2 cm" ->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=13⋅π⋅5 cm2⋅2 cm

V = "52.36 cm"^3V=52.36 cm3

Now, to find the density of the material, you must determine the mass of exactly "1 cm"^31 cm3 of material. To do that, use the fact that "52.36 cm"^352.36 cm3 of material have a mass of "6 g"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.

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