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

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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? 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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