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5/8/2015 10-4 B Volume and Surface Area of Composite Figures

COMPOSITE Figures:• A figure made up of two or more three-

dimensional shapes.

How to find Volume of composite shapes…

• Determine what individual shapes make up the larger shape itself.

• Find the volume of each shape separately.

• Add the volume of all of the shapes.

Example 1Find the volume of the composite figure. Use 3.14 for π.

Example 1

V = πr2hV ≈ 3.14 ● 2.52 ● 4V ≈ 78.5

V = bwh V = 5 ● 3 ● 7V = 105

Find the volume of each figure.

Rectangular Prism CylinderThe total volume is about 105 + 78.5 or 183.5 cubic inches.

Example 2A house is in the shape of the composite figure shown. Find the surface area of the composite figure.

The composite figure is made up of two different figures: a rectangular prism and a rectangular pyramid.

Prism

S.A. = 2bh + bw + 2hw

S.A. = 2(8 ● 8) + (8 ● 7) + 2(8 ● 7)

S.A. = 128 + 56 + 112

S.A. = 296

PyramidThe pyramid surfaces that you are finding are triangles with a height of 4 feet.Two of the triangles have a base of 8 feet and two have a base of 7 feet.

The total surface area of the figure is 296 + 60 or 356 square feet.

Example 3

What individual shapes make up the figure?

The stepping stool is made up of 2 different rectangular prisms. Find the volume of each prism.

Find the volume of each shape separately then add…

V = 16 • 12 • 7

V = 1,344

V = 10 • 12 • 7

V = 840

V = bwh V = bwh

Answer: The volume of the stepping stool is1,344 + 840 or 2,184 cubic inches.

Example 4

V = πr²h

V = πr²h 3

V = 84.8 ft³

Surface Area of Composite

Figures

How to find S.A. of composite shapes…

• Mentally separate the composite shape into their individual shapes.

• Find the S.A. of each shape.

• Add all of the surface areas together.

• Find the areas of each touching surface shape, then subtract those from the total S.A.

Example 5We are going to use our steps to find the surface area of the

stepping stool.

Mentally separate the composite shape into simpler individual shapes.

A = bh + bh

A = (14 • 10) + (6 • 7)

A = 182

Remember: there are 2 of these sides

A = bh

A = 10 • 12

A = 120

A = bh

A = 14 • 12

A = 168

Find the area of each outside surface of each shape.

A = Bh

A = 16 • 12

A = 192

A = Bh

A = 6 • 12

A = 72

A = Bh

A = 7 • 12

A = 84

Remember: there are 2 of these sides

Find the area of each outside surface of each shape.

Add all of the areas together.

The total surface area of the stepping stool is (2 • 182) + 120 + 168 + 192 + 72 + (2 • 84) or 1,084 square inches.

182 x2120

168

192 72 84 x2

Exit Ticket

2008.7m3

936in3

Homework

• Pg. 628 #1-20 Evens• Test Tuesday!