014 Water poured into a jar of marbles

Example 014
A boy who had discovered that 20 mm marbles fitted snugly into the bottom of a cylindrical jar, dropped in a fourth on top of the three and poured water enough into the jar to just cover them. How much water did he use?

012 Sphere circumscribed about a right circular cylinder

Example 012
Find the volume and total area of the sphere which circumscribes a cylinder of revolution whose altitude and diameter are each 6 inches.

03 - Heaviest cylinder that can be made from a shot

Problem 3
Find the weight of the heaviest circular cylinder can be cut from a 16-lb shot.

02 - Cylinder of maximum convex area inscribed in a sphere

Problem 02
A cylinder is inscribed in a given sphere. Find the shape of the cylinder if its convex surface area is a maximum.

The Right Circular Cylinder

A right circular cylinder is a cylinder whose base is a circle and whose elements are perpendicular to its base.

The Cylinder

Cylinder is a solid bounded by a closed cylindrical surface and two parallel planes.

Solids for which Volume = Area of base times Altitude

Solids in which V = Ab × h
This is a group of solids in which the volume is equal to the product of the area of the base and the altitude. Two types of solids belong to this group namely, prisms and cylinders.

62 - 63 Maxima and minima: cylinder inscribed in a cone and cone inscribed in a sphere

Problem 62
Inscribe a circular cylinder of maximum convex surface area in a given circular cone.