Volume of cylinders, Cones and Spheres

Front

What is the formula for the volume of a cylinder?

Back

V = πr²h, where V is volume, r is radius, and h is height.

Front

What is the formula for the volume of a cone?

Back

V = (1/3)πr²h, where V is volume, r is radius, and h is height.

Front

What is the formula for the volume of a sphere?

Back

V = (4/3)πr³, where V is volume and r is radius.

Front

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

Back

The volume increases by a factor of four (4) because volume is proportional to the square of the radius.

Front

What is the value of π (Pi) used in calculations?

Back

Approximately 3.14.

Front

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

Back

Rearrange the formula V = πr²h to find r: r = √(V/(πh)).

Front

What is the relationship between the radius and height in a cone?

Back

The volume of a cone depends on both the radius and height; changing either will affect the volume.

Front

How do you calculate the volume of a sphere with a radius of 5 cm?

Back

V = (4/3)π(5)³ = (4/3)π(125) ≈ 523.6 cm³.

Front

What is the volume of a cylinder with a radius of 3 ft and height of 10 ft?

Back

V = π(3)²(10) = 90π ≈ 282.74 ft³.

Front

What happens to the volume of a cone if the height is halved?

Back

The volume is halved, as volume is directly proportional to height.