   Chapter 9.4, Problem 36E 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

An observatory has the shape of a right circular cylinder surmounted by a hemisphere. If the radius of the cylinder is 14 ft and its altitude measures 30 ft, what is the surface area of the observatory? If 1 gallon of paint covers 300   f t   2 , how many gallons are needed to paint the surface if it requires two coats? Use your calculator. To determine

To find:

The surface area and number of gallons of paint required to paint an observatory.

Explanation

Formula Used:

The surface area of a hemisphere S = 2 πr2, where r is the radius of the sphere.

Curved or lateral surface area of a cylinder = 2πrh

Volume of cylinder = πr2h

Calculation:

Consider an observatory that has the shape of a right circular cylinder surmounted by a hemisphere.

The base radius of the cylinder (r) =14 ft and, altitude (h) =30 ft.

Surface area of observatory,

= Lateral surface area of right circular cylinder + Surface area of hemisphere

Surface area of observatory=2πrh+2πr2

Surface area of observatory S=2·3

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