11.4 Volume of 11.4 Volume of Prisms & CylindersPrisms & Cylinders

Exploring VolumeExploring Volume

• The volume of a solid is the number of cubic units contained in its interior (inside). Volume is measured in cubic units, such as cubic meters (m3).

Ex. 1: Finding the Volume of a rectangular prism

Finding Volumes of prisms and cylinders.

• Theorem 11.5 is named after Bonaventura Cavalieri (1598-1647).

Cavalieri’s PrincipleIf two solids have the same height and

the same cross-sectional area at every level, then they have the same volume.

Volume TheoremsVolume Theorems

• Volume of a Prism— The volume V of a prism is V=Bh, where B is the area of the base and h is the height.

• Volume of a Cylinder— The volume V of a cylinder is V=Bh=r2h, where B is the area of a base, h is the height, and r is the radius of the base.

Ex. 2: Finding Volumes

• Find the volume of the right prism.

V = Bh Volume of a prism formula

A = ½ bh Area of a triangleA = ½ (3)(4) Substitute valuesA = 6 cm2 Multiply values -- base

V = (6)(2) Substitute valuesV = 12 cm3 Multiply values & solve

Ex. 2: Finding Volumes

• Find the volume of the right cylinder.

V = Bh Volume of a prism formula

A = r2 Area of a circleA = 82 Substitute valuesA = 64 in.2 Multiply values -- base

V = 64(6) Substitute valuesV = 384in.3

Multiply values & solveV = 1206.37 in.3 Simplify

Ex. 3: Using Volumes

• Use the measurements given to solve for x.

Ex. 3: Using Volumes

• Use the measurements given to solve for x.