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

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

Back

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

Front

If a cone has a volume of 100 cm^3 and a height of 5 cm, what is the radius?

Back

Using V = \frac{1}{3} \pi r^2 h, we find r = \sqrt{\frac{300}{\pi}} \approx 9.8 cm.

Front

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

Back

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

Front

How does the volume of a cone change if the radius is doubled?

Back

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

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

If the height of a cone is tripled while keeping the radius constant, how does the volume change?

Back

The volume also triples, since V is directly proportional to height.