11.5 NOTES ­ Volume of Prisms and Cylinders

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LESSON 11.5 - Volume of Prisms and Cylinders

• The VOLUME of a solid is the number of cubic units contained in its interior.  

• Volume is measured in cubic units such as cubic meters (m3), cubic inches (in3), cubic yards (yd3), etc.

VOLUME OF A CUBEThe volume of a cube is the cube of the length of its side, or

V = s3

VOLUME CONGRUENCE POSTULATEIf two polyhedra are congruent, then they have the same volume.

VOLUME ADDITION POSTULATEThe volume of a solid is the sum of the volume of all its non‑overlapping parts.

How could you calculate the volume of this rectangular prism?

Multiply the number of blocks across by the number of blocks wide by the number of blocks tall.ORMultiply the area of the base by the height.ORMultiply the length by the width by the height.

VOLUME OF A PRISM

The volume V of a prism is 

V = Bhwhere B is the area of a base and h is the height.

Area of a Triangle =

Area of a Rectangle =

Area of a Trapezoid =

Area of a Circle =

bh

bh

(b1 + b2)h πr2

12

12

Find the volume of the prism.

V = 11 4 5

V = 220 m3

11.5 NOTES ­ Volume of Prisms and Cylinders

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Find the volume of the prism.

V = 3 4 2

V = 12 cm3

12

Find the volume of the prism.

V = ( (1.2 + 2.3)1.8)2

V = 6.3 cm3

12

V = ( (3.5)1.8)212

Find the volume of the cylinder.

V = (π(8)2)6

V = 384π

V = 1,206.4 in3

Find the volume of the solid.

V = ( π22)412

V = 25.1 in3

Semicircle cylinder:

Cube:

V = 43 = 64 in3

TOTAL:V = 25.1 in3 + 64 in3 = 89.1 in3

Calculate the volume of the cinder block.

V = 1.31 0.66 0.66 ENTIRE BLOCK VOLUME:

V = 0.57 ft3

V = 0.33 0.39 0.66 VOLUME OF ONE OF THE HOLES:

V = 0.08 ft3

V = 0.57 - 0.08 - 0.08

ACTUAL VOLUME OF THE CINDER BLOCK:

V = 0.41 ft3

How do you think the volumes of these two solids compare, given that their heights are equal, and the area of the given cross sections are equal?

Their volumes are equal!

11.5 NOTES ­ Volume of Prisms and Cylinders

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CAVALIERI'S PRINCIPLEIf two solids have the same height and the same cross‑sectional area at every level, then they have the same volume.

Find the volume of the oblique prism.

V = 6 11 14

V = 924 m3

Find the volume of the oblique cylinder.

V = (π  52)8

V = 628.3 ft3

Use the given information to solve for x.

100 = x3

cube root both sides to solve

x = 4.6 ft

Use the given information to solve for x.

4,561 = π  x2 12

120.98 = x2

12π12π

x = 10.999 m

square root both sides to solve

x = 11 m

HOMEWORK:11.5 Worksheet ‑ Volumes of Prisms and Cylinders