volume of cones, cylinders and spheres

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3) × π × r² × h, where r is the radius and h is the height.

Front

What is the formula for the volume of a cylinder?

Back

Volume = π × r² × h, 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) × π × r³, where r is the radius.

Front

If a cone has a radius of 3 cm and a height of 4 cm, what is its volume?

Back

Volume = (1/3) × π × (3)² × (4) = 12π cm³ ≈ 37.7 cm³.

Front

If a cylinder has a radius of 5 inches and a height of 10 inches, what is its volume?

Back

Volume = π × (5)² × (10) = 250π in³ ≈ 785.4 in³.

Front

If a sphere has a radius of 7 m, what is its volume?

Back

Volume = (4/3) × π × (7)³ = (4/3) × π × 343 ≈ 1436.8 m³.

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 1/3 of the volume 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.

Front

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

Back

Volume = (1/3) × π × (2)² × (6) = 8π cm³ ≈ 25.1 cm³.

Front

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

Back

Volume = π × (4)² × (5) = 80π m³ ≈ 251.3 m³.