Volume of a Cone

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 does the term 'radius' refer to in a cone?

Back

The radius is the distance from the center of the base of the cone to the edge of the base.

Front

What is the height of a cone?

Back

The height of a cone is the perpendicular distance from the base to the apex (the top point) of the cone.

Front

If a cone has a radius of 3 inches and a height of 9 inches, what is its volume?

Back

V = (1/3)π(3)²(9) = 27π ≈ 84.8 in³.

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 approximate volume of a cone with a radius of 5 inches and a height of 12 inches?

Back

V = (1/3)π(5)²(12) = 100π ≈ 314.2 in³.

Front

What is the relationship between the diameter and radius of a cone?

Back

The diameter is twice the radius. Diameter = 2 × Radius.

Front

If a cone has a diameter of 10 inches, what is its radius?

Back

The radius is half of the diameter, so the radius is 5 inches.

Front

What is the volume of a cone with a radius of 4 inches and a height of 14 inches?

Back

V = (1/3)π(4)²(14) = 74.7π ≈ 234.5 in³.