# 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 ?

Sep 6, 2017

Here's what I got.

#### Explanation:

Start by calculating the volume of the cone.

• $r = \text{5 cm} \to$ the radius of the cone
• $h = \text{2 cm} \to$ the height of the cone

Plug your values into the equation to get

$V = \frac{1}{3} \cdot \pi \cdot \text{5 cm"^2 * "2 cm}$

$V = {\text{52.36 cm}}^{3}$

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

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 ${\text{1 cm}}^{3}$ 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.