Video Transcript
The density of a material is calculated by dividing its mass by its volume. A particular cylinder has a height of three feet, a radius of two feet, and a mass of 200 pounds. Calculate the density of the cylinder, giving your answer to two decimal places.
We are reminded in the question that density is equal to mass divided by volume. We know that a particular cylinder has a mass of 200 pounds. At present, we donβt know its volume. We do know, however, that we can calculate the volume of any cylinder using the formula ππ squared β, where π is the radius and β the perpendicular height. Our cylinder has a height of three feet and a radius of two feet. Therefore, β equals three and π equals two. The volume π is therefore equal to π multiplied by two squared multiplied by three. Two squared is equal to four and multiplying this by three is 12. Therefore, π is equal to 12π. The volume of our cylinder is therefore equal to 12π cubic feet.
We always measure volume in cubic units, and as the height and radius of the cylinder are in feet, the volume will be in cubic feet. We can now calculate the density by dividing the mass by the volume. We need to divide 200 by 12π. This is equal to 5.3051 and so on. We need to round our answer to two decimal places, and as our deciding number is a five, we will round up.
The density of our cylinder is 5.31 pounds per cubic foot. The units for mass were pounds and the units for volume were cubic feet. Therefore, the units for density will be pounds per cubic foot.
