Volume part 3

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4R)/3dot Also find maximum volume in terms of volume of the sphere.

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?(i) Volume: 3x^2-12 x (ii) Volume: 12 k y^2+8k x-20 k

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3. Also, find maximum volume in terms of volume of the sphere.

There are two parts of a vessel. The pressure in one part is P and its volume is V. the volume of another part is 4V and there is vaccum in it. If the intervening wall is ruptured, then work done by the gas and change in its internal energy will be

A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air. At the equilibrium temperature of 320 K, the volume of upper and lower parts are in the ratio 4:1. The ratio of volume will become 3:1 at a temperature of

In the following pressure-volume diagram, the isochoric, isothermal and isobaric parts, respectively, are

A vertical cylinder of cross-sectional area 0.1m^(2) closed at both ends is fitted with a frictionless piston of mass M dividing the cylinder into two parts. Each part contains one mole of an ideal gas in equilibrium at 300K . The volume of the upper part is 0.1m^(3) and that of lower part is 0.05m^(3) .What force must be applied to the piston so that the volumes of the two parts remain unchanged when the temperature is increased to 500K ?

In the pressure-volume diagram given below, the isochoric, isothermal, isobaric, and isoentropic parts, respectively, are:

The volume of a sphere is (4pi)/(3) cm^(3) .Find the volume of that cube whose edge is equal to the diameter of the sphere.

coordination part 3