A right circular cylinder is inscribed in a given cone of radius R cm and height H cm as shown in the figure.
Find a relation connecting x and R when S is a maximum.

A right circular cylinder is inscribed in a given cone of radius R cm and height H cm as shown in the figure. Find the Surface area S of the circular cylinder as a function of x.

Rectangles are inscribed inside a semi-circle of radius r. Find the rectangle with maximum area.

A spherical surface of radius of curvature R, seperates a rarer and a denser medium as shown in the figure.Derive the relation connecting object distance .u., image distance .v., radius of curvature R and the refractive indices n_1 and n_2 of the two media.

The radius of a cylinder is increasing at a rate of 1 cm//s and its height decreasing at a rate of 1 cm//s . Find the rate of change of its volume when the radius is 5 cm and the height is 5 cm.

A metal sphere of radius R carrying q (+ve) charges is shown in the figure. br Draw the electric lines of force related to this metal sphere.

The radius of a cylinder increases at a rate of 1 cm/s and its height decreases at a rate of 1cm/s. Find the rate of change of its volume when the radius is 5 cm and the height is 15 cm. If the volume should not change even when the radius and height are changed, what is the relation between the radius and height?