Volume of prisms, pyramids, cylinders, cones, spheres

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 of the base and h is the height.

Front

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

Back

Rearrange the volume formula V = (1/3)πr²h to solve for r: r = sqrt((3V)/(πh)).

Front

What is the volume of a cylinder?

Back

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

Front

If a cone and a cylinder have the same base area and height, how do their volumes compare?

Back

The volume of the cylinder is three times the volume of the cone: V_cylinder = 3 * V_cone.

Front

What is the formula for the volume of a sphere?

Back

The volume V of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Front

How do you calculate the volume of a hemisphere?

Back

The volume V of a hemisphere is half the volume of a sphere: V = (2/3)πr³.

Front

What is the relationship between the volume of a cone and a pyramid with the same base area and height?

Back

The volume of the pyramid is one-third the volume of the cone: V_pyramid = (1/3)V_cone.

Front

How do you find the volume of a cone with a given radius and height?

Back

Use the formula V = (1/3)πr²h, substituting the values for r and h.

Front

What is the volume of a cylinder with a radius of 5 units and a height of 10 units?

Back

V = π(5)²(10) = 250π cubic units.

Front

If a cone has a height of 12 units and a radius of 4 units, what is its volume?

Back

V = (1/3)π(4)²(12) = 64π cubic units.