Volume of Cylinders

Front

What is the formula for the volume of a cylinder?

Back

Volume = πr²h, where r is the radius and h is the height.

Front

How do you find the radius of a cylinder if you know the diameter?

Back

Radius = Diameter / 2.

Front

If a cylinder has a height of 10 cm and a radius of 3 cm, what is its volume?

Back

Volume = π(3)²(10) = 90π cm³ or approximately 282.74 cm³.

Front

What is the relationship between the volume of a cylinder and its height?

Back

The volume increases linearly with height; if height doubles, volume doubles.

Front

What is the area of the base of a cylinder?

Back

Area = πr², where r is the radius of the base.

Front

If a cylinder has a radius of 5 cm and a height of 4 cm, what is the volume?

Back

Volume = π(5)²(4) = 100π cm³ or approximately 314.16 cm³.

Front

What is the volume of a cylinder with a diameter of 8 inches and a height of 10 inches?

Back

Volume = π(4)²(10) = 160π in³ or approximately 502.65 in³.

Front

How does the volume of a cylinder change if the radius is tripled?

Back

The volume increases by a factor of 9, since volume is proportional to the square of the radius.

Front

What is the volume of a cylinder that is 12 feet in diameter and 60 feet high, filled to 50%?

Back

Volume = π(6)²(60) = 2160π ft³; filled volume = 1080π ft³ or approximately 3391.2 ft³.

Front

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

Back

π is a constant that relates the diameter of a circle to its circumference and area.