You are offered two different rules for estimating the number of board feet in a 16-foot log. (A board foot is a unit of measure for lumber equal to a board 1 foot square and 1 inch thick.) One rule is modeled by V = (D − 4)2,  5 ≤ D ≤ 40, and the other rule is modeled by V = 0.8D2 − 2D − 4,  5 ≤ D ≤ 40, where D is the diameter (in inches) of the log and V is its volume (in board feet). For what diameter do the two rules agree? (Round your answer to two decimal places.)

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter26: Customary (english) Units Of Measure
Section: Chapter Questions
Problem 5A: The volume V of a cone with height h and diameter d is given by V=0.2618d2h . What is the volume of...
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You are offered two different rules for estimating the number of board feet in a 16-foot log. (A board foot is a unit of measure for lumber equal to a board 1 foot square and 1 inch thick.) One rule is modeled by V = (D − 4)2,  5 ≤ D ≤ 40, and the other rule is modeled by V = 0.8D2 − 2D − 4,  5 ≤ D ≤ 40, where D is the diameter (in inches) of the log and V is its volume (in board feet).

For what diameter do the two rules agree? (Round your answer to two decimal places.) 

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