8.G.9

Volume of Cylinders, Cones

and Spheres

What is VOLUME? The measure of the interior of a space (three-dimensional) figure.

A unit for measuring volume is the cubic unit (to the 3rd power.)

Simply the amount of space inside a 3D figure.

Mathematical Examples of Cylinders, Cones, and Spheres

Cylinder

Cone

Sphere

Real World Examples of Cylinders, Cones, and Spheres

Exact answers are left in terms of pi. Answer includes the pi symbol.

Approximate answers use 3.14 to multiply. Answer does not include the pi symbol.

Exact and Approximate Answers

V = 325π ft³

V = 125.41 in³

Exact

App

Finding the Volume of a Cylinder

2 in

4 in

V = πr²hV = π (2 in)² (4 in)V = π (4 in²) (4 in)

V = π (16 in³)V = 16π in³

V = 16(3.14) in³V = 50.24 in³

Exact

App

Bell Ringer What 3D figures are used to make the figure below?

Finding the Volume of a Cone

5 in

6 in

V = 1/3 πr²hV = 1/3 π (5 in)² (6 in)V = 1/3 π (25 in²) (6

in)V = 1/3 π (150 in³)

V = 50π in³V = 50(3.14) in³

V = 157 in³

Exact

App

Bell RingerDirections: Give exact and approximate answers.

Jill wants to fill a Campbell’s soup can with water but doesn’t know how much water she needs. If the cylindrical can has a radius of 1 inch and a height of 4 inches, what is the volume?

Jacob wants to put strawberry ice cream in his ice cream cone and doesn’t want to fill it above the rim. How much ice cream will be in the cone if it has a diameter of 4 inches and a height of 6 inches?

Bell Ringer Answers Campbell’s Soup Can:

Radius = 1 inchHeight = 4 inches

V = πr²hV = π (1 in)² (4 in)V = π (1 in²) (4 in)

V = π (4 in³)V = 4π in³

V = 4(3.14) in³V = 12.56 in³

Ice Cream Cone: Diameter = 4 inchesHeight = 6 inches

V = 1/3 πr²hV = 1/3 π (2 in)² (6 in)V = 1/3 π (4 in²) (6 in)

V = 1/3 π (24 in³)V = 8π in³

V = 8(3.14) in³V = 25.12 in³

Finding the Volume of a Sphere

24 in

V = 4/3 πr³V = 4/3 π (24 in)³V = 4/3 π (13824

in³)V = 18432π in³

V = 18432(3.14) in³V = 57876.48 in³

Exact

App