Volume of cylinders, Cones and 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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

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)πr³, 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 5 cm, what is its volume?

Back

Volume = (1/3)π(3)²(5) = 15π cm³ ≈ 47.12 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

If a sphere has a radius of 4 m, what is its volume?

Back

Volume = (4/3)π(4)³ = (4/3)π(64) ≈ 268.08 m³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

How do you convert the volume of a cylinder from cm³ to liters?

Back

1 liter = 1000 cm³, so divide the volume in cm³ by 1000.

Tags

CCSS.5.MD.A.1

Front

What is the volume of a cylinder with a radius of 2 cm and a height of 10 cm?

Back

Volume = π(2)²(10) = 40π cm³ ≈ 125.66 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the volume of a sphere with a diameter of 10 cm?

Back

Radius = 5 cm; Volume = (4/3)π(5)³ ≈ 523.6 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

If the radius of a cone is doubled, how does its volume change?

Back

The volume increases by a factor of 4, since volume is proportional to the square of the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3