Volume of Cones

Front

What is the formula for the volume of a cone?

Back

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

Front

If a cone has a radius of 3 cm and a height of 4 cm, what is its volume?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

What is the relationship between the height and volume of a cone?

Back

Volume is directly proportional to the height; increasing height increases volume.

Front

Calculate the volume of a cone with a radius of 2 cm and a height of 6 cm.

Back

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

Front

What units are used for measuring the volume of a cone?

Back

Cubic units, such as cm^3, m^3, in^3, etc.

Front

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

Back

The volume increases by a factor of 8, since volume is proportional to the square of the radius.

Front

What is the volume of a cone with a radius of 7.5 cm and a height of 5 cm?

Back

V = \frac{1}{3} \pi (7.5^2)(5) \approx 294.38 cm^3

Front

What is the volume of a cone with a radius of 1 m and a height of 3 m?

Back

V = \frac{1}{3} \pi (1^2)(3) = \pi \approx 3.14 m^3