# Value of x, volume of a cylinder

1) Using the graph, what is the value of x that will produce the maximum volume?

2) The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters.

Write h as a function of r.

https://brainmass.com/math/geometry-and-topology/value-of-x-volume-of-a-cylinder-82049

#### Solution Summary

This solution is comprised of a detailed explanation to answer what is the value of x that will produce the maximum volume.

Power Cycle for a Piston-Cylinder Device

A power cycle for a piston-cylinder device is described by the following four processes:

1→2 Isothermal compression from T1 = 300K, P1 = 100 kPa to P2 = 600 kPa.

2→3 Constant pressure heat addition until the temperature is T3 = 800K.

3→4 Isentropic expansion until the volume at state 4 equals the volume at state 1.

4→1 Constant volume heat rejection until the temperature is 300K.

Assume the working fluid is an ideal gas with constant specific heats and has properties as follows: CV = 0.600 kJ/(kg-K), CP = 0.900 kJ/(kg-K), R = 0.300 kJ/(kg-K), k = 1.500.

(a) Sketch the P-v diagram for this cycle

(b) Sketch the T-s diagram for this cycle

(c) Determine the heat rejected during process 1→2, in kJ/kg.

(d) Determine the heat added during process 2→3, in kJ/kg.

(e) Determine the total cycle expansion work done by the gas, in kJ/kg.

Could you please fill in this table, this will help organize all of the processes.

State P (kPa) T (K) V (m3/kg)

1 100 300

2 600 300

3 600 800

4