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 d 1 = 8 in . and s = 17 in . and a lower base of dimensions d 2 = 20 in . and s = 17 in . . Substitute the values d 1 = 8 in ., d 2 = 20 in . , s = 17 in . and h = 16 in . in the equation L = 1 2 π s ( d 1 + d 2 ) and obtain the total surface area of the frustum as follows: L = 1 2 π s ( d 1 + d 2 ) = 1 2 ⋅ ( 3.14 ) ⋅ ( 17 ) ⋅ ( 8 + 20 ) = 747.62 ≈ 748 sq in . ( Rounded ) Thus, the lateral surface area of the frustum is 748 sq in . . Substitute r 1 = 4 in . in the formula A 1 = π r 1 2 and calculate the area of the upper base of the frustum as follows: A 1 = π r 1 2 ( r = d 2 ) = π ⋅ ( 4 ) 2 = 16 π Substitute r 2 = 10 in

10th Edition

ISBN: 8220100803055

Author: SAUNDERS

Publisher: PEARSON

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Question

Chapter 9.4, Problem 3BE

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 2BE

Chapter 9.4, Problem 4BE

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Chapter 9 Solutions

EBK MATHEMATICS FOR THE TRADES

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