Calculating Volume and Weight of Cylinders

Vincent explains a volume density word problem involving calculating the total weight of exercise equipment. The problem requires understanding the volume of a cylinder and converting units from inches to feet to match the density units. Vincent demonstrates how to calculate the weight of sand added to a base filled to 85% capacity and provides an alternate solution using cubic inches. The video concludes with a call to action for viewers to like and subscribe.

What is the main task described in the problem setup?

• Find the density of the sand used.

• Calculate the volume of the exercise equipment.

• Determine the total weight of the exercise equipment.

• Measure the height of the cylinder.

How do you calculate the radius of the cylinder if the diameter is given?

• Multiply the diameter by two.

• Subtract the height from the diameter.

• Divide the diameter by two.

• Add the diameter and height.

Why is it necessary to convert the radius and height from inches to feet?

• To avoid using fractions.

• To reduce the size of the numbers.

• To make the calculations easier.

• To match the units of density which are in cubic feet.

What percentage of the base is filled with sand?

• 100%

• 50%

• 85%

• 75%

What is the formula used to calculate the volume of a cylinder?

• R squared times H

• pi times R squared times H

• 2 times pi times R times H

• pi times D times H

How is the weight of the sand calculated?

• By subtracting the density from the volume of sand.

• By dividing the volume of sand by its density.

• By multiplying the volume of sand by its density.

• By adding the volume and density of the sand.

What is the total weight of the exercise equipment after adding the sand?

• 536 pounds

• 270 pounds

• 500 pounds

• 266 pounds

In the alternate solution, what conversion factor is used for cubic inches to cubic feet?

• 1 foot over 1728 inches

• 1 foot over 144 inches

• 1 foot over 1000 inches

• 1 foot over 12 inches

What is the volume of sand in cubic inches if the radius and height are not converted to feet?

• 1530 PI cubic inches

• 1000 PI cubic inches

• 500 PI cubic inches

• 2000 PI cubic inches

What is the final answer for the total weight of the exercise equipment?

• 600 pounds

• 536 pounds

• 500 pounds

• 450 pounds