Question

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` ?

Answer 1

Here's what I got.

Explanation:

Start by calculating the volume of the cone.

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.