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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the formula for the volume of a sphere?

Back

Volume = (4/3) × π × r³, where r is the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.3.MD.A.2

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3