Volume Formulas and Calculations

Mr. West guides students through solving volume word problems involving cylinders, spheres, and cones. The video covers calculating the volume of a cylindrical water bottle, determining the height of a smaller paint can, finding the height of a new cone with the same volume, and calculating the total volume of multiple gumballs. The tutorial aims to simplify complex problems and enhance understanding of volume calculations.

What is the formula for the volume of a cylinder?

• 1/3πr²h

• 4/3πr³

• πr²h

• 2πr²

If a cylinder has a radius of 4 cm and a height of 20 cm, what is its volume in terms of π?

• 320π cm³

• 80π cm³

• 160π cm³

• 640π cm³

How much paint is left in Jameel's can if he has used three-fourths of it?

• Three-fourths of the can

• Half of the can

• The entire can

• One-fourth of the can

What is the formula for the volume of a cone?

• 2πr²

• 4/3πr³

• πr²h

• 1/3πr²h

If a cone has a radius of 2 cm and a height of 6 cm, what is its volume in terms of π?

• 8π cm³

• 12π cm³

• 16π cm³

• 24π cm³

What is the height of the new cone if it has the same volume as the original cone with a radius of 4 cm?

• 2 inches

• 3 inches

• 1.5 inches

• 4 inches

What is the formula for the volume of a sphere?

• 4/3πr³

• πr²h

• 1/3πr²h

• 2πr²

If the radius of a sphere is 6 mm, what is its volume in terms of π?

• 216π mm³

• 432π mm³

• 144π mm³

• 288π mm³

How many gumballs did Stacey receive from the machine?

• Four

• One

• Three

• Two

What is the total volume of four gumballs, each with a radius of 6 mm, in terms of π?

• 1152π mm³

• 576π mm³

• 288π mm³

• 864π mm³