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

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
12 views

# 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.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 