Volume of a Cone Class Practice

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3) * π * r² * h, where r is the radius and h is the height.

Front

If the radius of a cone is doubled, how does the volume change?

Back

The volume increases by a factor of 4, since volume is proportional to the square of the radius.

Front

What does 'h' represent in the volume formula for a cone?

Back

'h' represents the height of the cone.

Front

Calculate the volume of a cone with a radius of 3 inches and a height of 4 inches.

Back

Volume = (1/3) * π * (3)² * (4) = 12π ≈ 37.70 cubic inches.

Front

What is the relationship between the diameter and radius of a cone?

Back

The radius is half of the diameter.

Front

How do you find the area of the base of a cone?

Back

Area = π * r², where r is the radius of the base.

Front

What is the volume of a cone with a height of 10 cm and a radius of 5 cm?

Back

Volume = (1/3) * π * (5)² * (10) = 83.33 cm³.

Front

What is the significance of π in the volume formula of a cone?

Back

π is a constant that represents the ratio of the circumference of a circle to its diameter, essential for calculations involving circles.

Front

If a cone has a volume of 150 cm³ and a height of 6 cm, what is the radius?

Back

Using the formula, r = √((3 * Volume) / (π * h)) = √((3 * 150) / (π * 6)) ≈ 4.24 cm.

Front

What is the volume of a cone with a radius of 2 inches and a height of 3 inches?

Back

Volume = (1/3) * π * (2)² * (3) = 4π ≈ 12.57 cubic inches.