Could you please show me how to solve this problem ! A soil sample is 5.08 cm in diameter and 47.3 mm high. Find volume in cm^3. Also find density (g/cm^3) if its mass is 137.33 g.
To find the volume of the soil sample, we need to use the formula for the volume of a cylinder. The formula for the volume of a cylinder is given by:
V = πr^2h
Where V is the volume, r is the radius, and h is the height of the cylinder.
First, let's convert the diameter of the soil sample from centimeters to millimeters. Since there are 10 millimeters in 1 centimeter, the diameter of 5.08 cm is equal to 5.08 * 10 = 50.8 mm.
To find the radius of the cylinder, we need to divide the diameter by 2. So the radius (r) of the soil sample is 50.8 mm / 2 = 25.4 mm.
Next, let's convert the height of the soil sample from millimeters to centimeters. Since there are 0.1 centimeters in 1 millimeter, the height of 47.3 mm is equal to 47.3 * 0.1 = 4.73 cm.
Now, we can substitute the values into the formula for the volume of a cylinder:
V = π * (25.4 cm)^2 * 4.73 cm
Calculating this expression will give us the volume of the soil sample in cubic centimeters (cm^3).
V ≈ 3.14159 * 25.4^2 * 4.73 ≈ 9,600.55 cm^3
Therefore, the volume of the soil sample is approximately 9,600.55 cm^3.
To find the density of the soil sample, we need to use the formula:
Density = mass / volume
Given that the mass of the soil sample is 137.33 g and we just calculated the volume as 9,600.55 cm^3, we can substitute these values into the formula to find the density:
Density = 137.33 g / 9,600.55 cm^3
Calculating this expression will give us the density of the soil sample in grams per cubic centimeter (g/cm^3).