## 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.

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.

- Read more about 03 - Heaviest cylinder that can be made from a shot
- Log in or register to post comments

**Problem 02**

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

**Situation**

A right circular cylinder of radius r and height h is inscribed in a right circular cone of radius 6 m and height 12 m.

Part 1: Determine the radius of the cylinder such that its volume is a maximum.

A. 2 m

B. 4 m

C. 3 m

D. 5 m

Part 2: Determine the maximum volume of the cylinder.

A. 145.72 m^{3}

B. 321.12 m^{3}

C. 225.31 m^{3}

D. 201.06 m^{3}

Part 3: Determine the height of the cylinder such that its lateral area is a maximum.

A. 10 m

B. 8 m

C. 6 m

D. 4 m

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.

**Problem 63**

Find the circular cone of maximum volume inscribed in a sphere of radius *a*.

**Problem 53**

Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.

**Problem 54**

A cylindrical tin boiler, open at the top, has a copper bottom. If sheet copper is m times as expensive as tin, per unit area, find the most economical proportions.

**Problem 55**

Solve Problem 54 above if the boiler is to have a tin cover. Deduce the answer directly from the solution of Problem 54.

- Read more about 53 - 55 Solved Problems in Maxima and Minima
- Log in or register to post comments

**Problem 38**

A cylindrical glass jar has a plastic top. If the plastic is half as expensive as glass, per unit area, find the most economical proportion of the jar.

**Problem 39**

A trapezoidal gutter is to be made from a strip of tin by bending up the edges. If the cross-section has the form shown in Fig. 38, what width across the top gives maximum carrying capacity?

**Problem 40**

Solve Ex. 39, if the strip is 11 inches wide and the base is 7 inches wide.

- Read more about 38 - 40 Solved problems in maxima and minima
- Log in or register to post comments

**Problem 29**

The sum of the length and girth of a container of square cross section is a inches. Find the maximum volume.

**Problem 30**

Find the proportion of the circular cylinder of largest volume that can be inscribed in a given sphere.

**Problem 31**

In Problem 30 above, find the shape of the circular cylinder if its convex surface area is to be a maximum.

- Read more about 29 - 31 Solved problems in maxima and minima
- Log in or register to post comments

**Problem 25**

Find the most economical proportions of a quart can.

**Problem 26**

Find the most economical proportions for a cylindrical cup.

**Problem 27**

Find the most economical proportions for a box with an open top and a square base.

- Read more about 25 - 27 Solved problems in maxima and minima
- Log in or register to post comments

**Problem 42**

From a cylindrical glass 6 in. high and 3 in. in diameter, water is poured by tilting the glass until the highest point of the bottom of the glass lies in the plane of the water surface. How much water remains?

**Problem 13**

The accompanying figure represents the longitudinal view of a Venturi meter, a device designed to measure the flow of water in pipes. If the throat of the of the meter is 6 in. long and has an inside diameter of 4 in., find the volume of water in the meter which is used in 12-in. pipe line if the altitudes of the tapering parts are in the ratio 1:3 and the smaller altitude measures 12 in.