Volume of Cones, Cylinders, Spheres

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base 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

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius of the base 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

The volume V of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

How do you convert diameter to radius?

Back

The radius is half of the diameter. To find the radius, divide the diameter by 2.

Tags

CCSS.7.G.B.4

Front

If a cylinder has a height of 10 inches and a radius of 3 inches, what is its volume?

Back

The volume is V = π(3)²(10) = 90π ≈ 282.74 cubic inches.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the relationship between the height and radius in the volume formulas for cones and cylinders?

Back

Both formulas include height (h) and radius (r) as variables, but the cone's volume is one-third that of a cylinder with the same base and height.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the significance of π in volume calculations?

Back

π (pi) is a mathematical constant approximately equal to 3.14159, used in formulas involving circles and spheres.

Tags

CCSS.HSG.GMD.A.1

Front

How do you find the volume of a cone with a radius of 4 inches and a height of 9 inches?

Back

Use the formula V = (1/3)π(4)²(9) = 48π ≈ 150.8 cubic inches.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

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

Back

Using the formula V = (4/3)π(5)³ = (4/3)π(125) ≈ 523.6 cubic inches.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the volume of a cylinder with a radius of 2 inches and a height of 6 inches?

Back

The volume is V = π(2)²(6) = 24π ≈ 75.4 cubic inches.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3