Volume of Cones and Cylinders

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height.

Front

What is the formula for the volume of a cylinder?

Back

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

Front

What does π (pi) represent in geometry?

Back

π (pi) is a mathematical constant approximately equal to 3.14, representing the ratio of the circumference of a circle to its diameter.

Front

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

Back

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

Front

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

Back

The volume of a cone is directly proportional to its height; if the height increases, the volume increases.

Front

How do you find the radius if you know the volume of a cone?

Back

Rearranging the volume formula V = (1/3)πr²h gives r = sqrt((3V)/(πh)).

Front

What is the volume of a cone with a radius of 3 cm and a height of 10 cm?

Back

Using the formula V = (1/3)πr²h, the volume is approximately 28.3 cm³.

Front

What is the volume of a cylinder with a diameter of 10 cm and a height of 5 cm?

Back

The radius is 5 cm, so the volume is V = π(5)²(5) = 125π ≈ 392.7 cm³.

Front

What shape is formed when a cone is rotated around its height?

Back

When a cone is rotated around its height, it forms a three-dimensional shape called a cone.

Front

What is the effect of increasing the height of a cylinder on its volume?

Back

Increasing the height of a cylinder increases its volume proportionally.