Volume of Cylinders, Cones, & Spheres

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base and h is the height.

Front

What is the formula for the volume of a sphere?

Back

The volume V of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Front

If a cylinder has a radius of 3 cm and a height of 5 cm, what is its volume?

Back

The volume is V = π(3)²(5) = 45π cm³, approximately 141.37 cm³.

Front

If a cone has a radius of 4 cm and a height of 6 cm, what is its volume?

Back

The volume is V = (1/3)π(4)²(6) = 32π cm³, approximately 100.53 cm³.

Front

If a sphere has a radius of 5 cm, what is its volume?

Back

The volume is V = (4/3)π(5)³ = (500/3)π cm³, approximately 523.6 cm³.

Front

What is the relationship between the volume of a cone and a cylinder with the same base and height?

Back

The volume of the cone is one-third the volume of the cylinder.

Front

How does increasing the height of a cylinder affect its volume?

Back

Increasing the height of a cylinder increases its volume proportionally, as volume is directly related to height.

Front

How does increasing the radius of a sphere affect its volume?

Back

Increasing the radius of a sphere increases its volume significantly, as volume is proportional to the cube of the radius.

Front

What units are used to measure volume?

Back

Common units for measuring volume include cubic centimeters (cm³), cubic meters (m³), and liters (L).