Show that a cylinder of a given volume, which is open at the top has minimum total surface area, when its height is equal to the radius of its base.

A body weighs one Newton at the surface of the earth. What will be it’s weight at a height equal to half the radius of the earth ?

Show that the right circular cone of least curved surface area and given volume has an altitude equal to sqrt(2) times the radius of the base.

Show that the semivertical angle of a cone of given slant height is tan^1 sqrt2 when its volume is maximum.

Show that area of a parallelogram formed , with two vectors as its adjacent sides , is equal to the magnitude of their cross product.

Show that the radius of the right cicular cylinder of greatest curved surface that can be inscribed in a given cone is half the redius of the base of the cone.

If a person goes (i) to a height equal to radius earth and below its surface what would be his weight in the two cases relative to earth ?

The radius of a spherical soap bubble is increasing at the rate of 0.2cm/sec. Find the rate of increase of its surface area, when the radius is 7cm. ( pi=3.141 approx)

Show that the height of a closed right circular cylinder of given surface and maximum volume is equal to diameter of base.