Volume of Cones

Front

What is the formula for the volume of a cone?

Back

V = \frac{1}{3} \pi r^2 h

Front

What does 'r' represent in the volume formula of a cone?

Back

The radius of the base of the cone.

Front

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

Back

The height of the cone.

Front

How do you calculate the volume of a cone with a radius of 3 cm and a height of 4 cm?

Back

V = \frac{1}{3} \pi (3^2)(4) = 12\pi \approx 37.7 cm^3.

Front

If a cone has a radius of 5 cm and a height of 10 cm, what is its volume?

Back

V = \frac{1}{3} \pi (5^2)(10) = \frac{250}{3}\pi \approx 261.8 cm^3.

Front

What is the volume of a cone with a radius of 2 m and a height of 6 m?

Back

V = \frac{1}{3} \pi (2^2)(6) = \frac{24}{3}\pi = 8\pi \approx 25.1 m^3.

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 that of the cylinder.

Front

How does changing the radius of a cone affect its volume?

Back

Increasing the radius increases the volume, as volume is proportional to the square of the radius.

Front

How does changing the height of a cone affect its volume?

Back

Increasing the height increases the volume, as volume is directly proportional to the height.

Front

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

Back

V = \frac{1}{3} \pi (4^2)(9) = \frac{144}{3}\pi = 48\pi \approx 150.8 in^3.