if a coin with 3.0 cm diameter, 0.2 cm thickness weighs 10.377g, what are its volume and density?
volume = pi*r^2*thickness.
density = mass/volume.
To find the volume and density of the coin, we need to use a few formulas and calculations.
First, let's find the volume of the coin. The formula for the volume of a cylinder (which is similar to the shape of a coin) is:
Volume = π * r^2 * h
where π is the mathematical constant approximately equal to 3.14159, r is the radius of the coin, and h is the height or thickness of the coin.
In this case, the diameter of the coin is given as 3.0 cm, so we can calculate the radius using the formula:
Radius = diameter / 2 = 3.0 cm / 2 = 1.5 cm
The thickness or height of the coin is given as 0.2 cm.
Now, we can substitute the values into the volume formula:
Volume = π * (1.5 cm)^2 * 0.2 cm
Calculating this will give us the volume of the coin.
Next, let's find the density of the coin. Density is defined as mass per unit volume, so we can use the formula:
Density = mass / volume
We are given the mass of the coin as 10.377 g, which we'll use for the numerator in the formula. We calculated the volume in the previous step, so we'll use that value for the denominator.
Finally, we can substitute the values and calculate the density of the coin.
By following these steps, we can find the volume and density of the given coin.