Volume of Cylinders, Cones, & Spheres

Front

What is the formula for the volume of a cylinder?

Back

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

Front

What is the formula for the volume of a cone?

Back

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

Front

What is the formula for the volume of a sphere?

Back

Volume = (4/3)πr³, where r is the radius.

Front

How do you approximate π for calculations?

Back

Use 3.14 as an approximation for π.

Front

What is the volume of a cylinder with a radius of 2 ft and a height of 5 ft?

Back

Volume = π(2)²(5) = 20π ≈ 62.8 ft³.

Front

What is the volume of a cone with a radius of 3 cm and a height of 4 cm?

Back

Volume = (1/3)π(3)²(4) = 12π ≈ 37.68 cm³.

Front

What is the volume of a sphere with a radius of 5 m?

Back

Volume = (4/3)π(5)³ = (4/3)π(125) ≈ 523.6 m³.

Front

If a cylinder has a volume of 1000 ft³ and a height of 10 ft, what is its radius?

Back

Radius r = √(Volume / (πh)) = √(1000 / (π * 10)) ≈ 5.64 ft.

Front

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

Back

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

Front

How does changing the radius of a cylinder affect its volume?

Back

Increasing the radius increases the volume exponentially, as volume is proportional to the square of the radius.