Volume of Cylinders and Cones

Front

What is the formula for the volume of a cylinder?

Back

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

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 ≈ 785.4 units³.

Front

What is the formula for the volume of a cone?

Back

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

Front

What is the volume of a cone with a radius of 3 units and a height of 9 units?

Back

V = (1/3)π(3)²(9) = 27π ≈ 84.8 units³.

Front

What does the symbol π represent in volume formulas?

Back

π (pi) is a mathematical constant approximately equal to 3.14, representing the ratio of a circle's circumference to its diameter.

Front

How do you find the volume of a cylinder?

Back

Multiply the area of the base (πr²) by the height (h).

Front

If a cylinder has a volume of 1000 units³ and a height of 10 units, what is the radius?

Back

Using V = πr²h, we find r = √(V/(πh)) = √(1000/(π*10)) ≈ 5.64 units.

Front

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

Back

The volume of the cone is one-third that of the cylinder.

Front

What is the volume of a cylinder with a radius of 4 units and a height of 5 units?

Back

V = π(4)²(5) = 80π ≈ 251.3 units³.

Front

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

Back

V = (1/3)π(2)²(6) = 8π ≈ 25.1 units³.