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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 9.4, Problem 23E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons.

With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9   c m 2 and area of each regular hexagon is 52.5   c m 2 .

a) What is the surface area of the soccer ball?

b) If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?

Chapter 9.4, Problem 23E, The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each

To determine

To find:

The surface area of the soccer ball.

Explanation

Approach:

1) A polygon is a two dimensional shape form with more than two straight lines.

2) A polyhedron is a three-dimensional solid shape.

3) Each flat surface of a polyhedron is a polygon and is called a face.

4) The line segment where two faces of a polyhedron meet is called an edge.

5) The point where three or more edges of a polyhedron meet is called a vertex.

6) A regular polyhedron is a convex polyhedron whose faces are congruent regular polygons.

Calculation:

A closed figure with five equal sides and angles is called a regular pentagon.

A closed figure with six equal sides and angles is called a regular hexagon.

Area of each regular pentagon is 34.9 cm2.

Area of each regular hexagon is 52.5 cm2.

The surface area of the soccer ball = Surface area of 12 regular pentagons+ Surface area of 20 regular hexagons

=12·34

To determine

To find:

The cost of the material used to construct a soccer ball.

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