Volume of Cones and Cylinders

Front

What is the formula for the volume of a cone?

Back

The volume 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 cylinder?

Back

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

Front

If a cone has a radius of 3 inches and a height of 5 inches, what is its volume?

Back

V = (1/3)π(3)²(5) = 15π ≈ 47.1 cubic inches.

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 do you calculate the radius if you know the diameter?

Back

The radius is half of the diameter. r = diameter/2.

Front

What is π (pi) approximately equal to?

Back

π is approximately equal to 3.14.

Front

What is the volume of a cylinder with a diameter of 10 cm and a height of 20 cm?

Back

First, find the radius: r = 10/2 = 5 cm. Then, V = π(5)²(20) = 500π ≈ 1570 cubic cm.

Front

What units are used to measure volume?

Back

Volume is typically measured in cubic units, such as cubic inches, cubic centimeters, or liters.

Front

What is the volume of a cone with a radius of 4 inches and a height of 9 inches?

Back

V = (1/3)π(4)²(9) = 48π ≈ 150.8 cubic inches.

Front

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

Back

V = π(3)²(10) = 90π ≈ 282.7 cubic cm.