Volume of Cylinder, Cone, and Sphere

Front

What is the formula for the volume of a cone?

Back

V = (1/3)πr²h

Front

How do you calculate the volume of a cylinder?

Back

V = πr²h

Front

What is the formula for the volume of a sphere?

Back

V = (4/3)πr³

Front

If the radius of a cone is 3 cm and the height is 10 cm, what is its volume?

Back

V = (1/3)π(3)²(10) = 30π ≈ 94.25 cm³

Front

What is 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

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

Back

Use the formula r = (3V/(4π))^(1/3) to find the radius.

Front

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

Back

The radius is half of the diameter (r = d/2).

Front

If a cylinder has a height of 7 cm and a radius of 4 cm, what is its volume?

Back

V = π(4)²(7) = 112π ≈ 351.86 cm³

Front

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

Back

V = (1/3)π(2)²(6) = 8π ≈ 25.13 cm³

Front

How does increasing the radius of a sphere affect its volume?

Back

The volume increases with the cube of the radius (V ∝ r³).