Question

The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function A(x) = 4x(sqrt{1 - x^2}), where x represents the length of half the base of the beam. Determine the cross-sectional area of the beam if the length of half the base of the beam is 1/3 of a foot.

Answer 1

A = 4 (1/3)sqrt (1 - 1/9)
= (4/3)sqrt (8/9)
= (4/3)sqrt (4 *2/9)
= (4/3)(2/3) sqrt(2)
= (8/9)sqrt(2)