Minimum painting surface A metal cistern in the shape ofa right circular cylinder with volume V = 50 m3 needs to bepainted each year to reduce corrosion. The paint is applied onlyto surfaces exposed to the elements (the outside cylinder wall andthe circular top). Find the dimensions r and h of the cylinder thatminimize the area of the painted surfaces.
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.
Minimum painting surface A metal cistern in the shape of
a right circular cylinder with volume V = 50 m3 needs to be
painted each year to reduce corrosion. The paint is applied only
to surfaces exposed to the elements (the outside cylinder wall and
the circular top). Find the dimensions r and h of the cylinder that
minimize the area of the painted surfaces.
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