Volume of Cylinders, Cones, Spheres, & Composite Shapes

Front

What is the formula for the volume of a cylinder?

Back

V = πr²h, 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 cone?

Back

V = 1/3πr²h, 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

V = 4/3πr³, where r is the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

How do you find the volume of a composite shape?

Back

Calculate the volume of each individual shape and then sum them up.

Tags

CCSS.5.MD.C.5C

Front

If a cylinder has a radius of 3 cm and a height of 5 cm, what is its volume?

Back

V = π(3)²(5) = 45π cm³ ≈ 141.37 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

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

Back

V = 1/3π(4)²(9) = 48π cm³ ≈ 150.8 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the volume of a sphere with a radius of 6 cm?

Back

V = 4/3π(6)³ = 288π cm³ ≈ 904.32 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the combined volume of a cylinder with a volume of 200 cm³ and a cone with a volume of 100 cm³?

Back

Combined volume = 200 cm³ + 100 cm³ = 300 cm³.

Tags

CCSS.5.MD.C.5C

Front

What is the height of a cylinder if its volume is 600 cm³ and the radius is 5 cm?

Back

Using V = πr²h, h = V / (πr²) = 600 / (π(5)²) ≈ 7.64 cm.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the volume of a composite shape made of a cylinder and a cone if the cylinder's volume is 500 cm³ and the cone's volume is 200 cm³?

Back

Total volume = 500 cm³ + 200 cm³ = 700 cm³.

Tags

CCSS.5.MD.C.5C