Chapter 9.4, Problem 23E

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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

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

Area of each regular hexagon is

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

=

To determine

**To find:**

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

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