Volume A trough is 16 feet long (see figure). Its cross sections are isosceles triangleswith each of the two equal sides measuring 18 incites. The angle between the twoequal sides is θ(a) Write the volume of the trough as a function of θ and determine the value of θ suchthat the volume is a maximum.(b) The maximum error in the linear measurements is one-half inch and themaximum error in the angle measure is 2o. Approximate the change in tlie maximumvolume
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Volume A trough is 16 feet long (see figure). Its cross sections are isosceles triangles
with each of the two equal sides measuring 18 incites. The angle between the two
equal sides is θ
(a) Write the volume of the trough as a function of θ and determine the value of θ such
that the volume is a maximum.
(b) The maximum error in the linear measurements is one-half inch and the
maximum error in the angle measure is 2
o
. Approximate the change in tlie maximum
volume
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