Volume of Cone, Cylinder & Sphere Flashcard

Front

What is the formula for the volume of a cone?

Back

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

Front

What is the formula for the volume of a sphere?

Back

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

Front

If the radius of a cone is 3 inches and the height is 5 inches, what is its volume?

Back

Using the formula V = (1/3)πr²h, the volume is V = (1/3)π(3)²(5) = 15π ≈ 47.1 in³.

Front

What is the diameter of a circle if the radius is 5 inches?

Back

The diameter is twice the radius, so the diameter is 10 inches.

Front

How do you convert the volume of a cylinder from cubic inches to liters?

Back

To convert cubic inches to liters, multiply by 0.0163871.

Front

What is the volume of a cone with a radius of 4 inches and a height of 9 inches?

Back

Using the formula V = (1/3)πr²h, the volume is V = (1/3)π(4)²(9) = 48π ≈ 150.8 in³.

Front

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

Back

The diameter is twice the radius (d = 2r).

Front

If a cylinder has a volume of 100 in³ and a height of 10 inches, what is the radius?

Back

Using the formula V = πr²h, rearranging gives r = √(V/(πh)). For V = 100 and h = 10, r ≈ 1.79 inches.

Front

What is the volume of a sphere with a radius of 3 inches?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3)π(3)³ = 36π ≈ 113.1 in³.