Explanation Formula used: The lateral surface area of a cone is given by L = π s ( r 1 + r 2 ) or L = 1 2 π s ( d 1 + d 2 ) where r 1 is the radius of the upper base, r 2 is the radius of the lower base, d 1 is the diameter of the upper base, d 2 is the diameter of the lower base and s is the slant height. The volume of the cone is given by the formula V = 1 3 π h ( r 1 2 + r 2 2 + r 1 r 2 ) or V = π h 12 ( d 1 2 + d 2 2 + d 1 d 2 ) where r 1 is the radius of the upper base, r 2 is the radius of the lower base, d 1 is the diameter of the upper base, d 2 is the diameter of the lower base and h is the altitude. Total surface area is given by S = L + A 1 + A 2 . Calculation: From the given figure, it is to be noted that the given solid object is a frustum with upper base of dimensions r 1 = 4.5 ft and s = 5 ft and a lower base of dimensions r 2 = 7.5 ft and s = 5 ft . Substitute the values r 1 = 4.5 ft, r 2 = 7.5 ft , h = 4 ft and s = 5 ft in the equation L = 1 3 π h ( r 1 2 + r 2 2 + r 1 r 2 ) and obtain the total surface area of the frustum as follows: L = π s ( r 1 + r 2 ) = ( 3.14 ) ⋅ ( 5 ) ⋅ ( 4.5 + 7.5 ) = 188.4 ≈ 188 sq ft ( rounded ) Thus, the lateral surface area of the frustum is 188 sq ft . Substitute r 1 = 4.5 ft in the formula A 1 = π r 1 2 and calculate the area of the upper base as follows: A 1 = π r 1 2 = π ⋅ ( 4

10th Edition

ISBN: 8220100803055

Author: SAUNDERS

Publisher: PEARSON

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Question

Chapter 9.4, Problem 4BE

To determine

The total surface area and volume of the given solid object and to round the result to three significant digits.

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Chapter 9.4, Problem 3BE

Chapter 9.4, Problem 1CE

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Chapter 9 Solutions

EBK MATHEMATICS FOR THE TRADES

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