Exploring Volume Calculations for Cylinders, Cones, and Spheres

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

• V = πr^3

• V = 4/3πr^3

• V = πr^2h

• V = 1/3πr^2h

How can you demonstrate that the volume of a cone is one-third that of a cylinder with the same base and height?

• By measuring their weights

• By filling the cone with water and pouring it into the cylinder three times

• By comparing their surface areas

• By calculating their base areas

How does the volume of a cone compare to that of a cylinder with the same base and height?

• It is half

• It is three times larger

• It is the same

• It is one-third

What demonstrates that the volume of a cone is one-third the volume of a cylinder with the same base and height?

• Filling the cone with water three times to fill the cylinder

• Measuring their diameters

• Calculating their surface areas

• Comparing their weights

What is the volume of a cylinder with a radius of 3 units and a height of 4 units, expressed in terms of π?

• 36π units^3

• 12π units^3

• 48π units^3

• 9π units^3

Why do we often leave π in our answers when calculating volumes?

• For greater accuracy

• Because it's easier to write

• To simplify calculations

• All of the above

What is the volume of a cone with a radius of 3 units and a height of 4 units, using 3.14 for π and rounded to the nearest tenth?

• 113.1 units^3

• 12.6 units^3

• 36.0 units^3

• 37.7 units^3

What is the formula to calculate the volume of a sphere?

• V = πr^3

• V = 4/3πr^3

• V = 1/3πr^2h

• V = πr^2h

What unique property does a sphere have compared to cylinders and cones?

• It only requires the radius to calculate volume

• It is two-dimensional

• It has a height

• It has a base area

What is the volume of a sphere with a radius of 3 units, expressed in terms of π?

• 36π units^3

• 27π units^3

• 108π units^3

• 9π units^3