A figure consists of a semi-circle with a rectangle on its diameter. Given that the perimeter of the figure is 20 cm. Find the dimensions in order that its area may be maximuum.

The lengths of the largest side of a quadrilateral is three times that of its smallest side. Out of the other two sides length of one is twice that of the smallest and the other is 1 cm. longer than the smallest. If the perimeter of the quadrilateral is at most 36 cm. then find the maximum possible lengths of its sides.

The length of one side of a parallelogram is 1 cm. shorter than that of its adjacent side. If its perimeter is at least 26 cm. find the minimum possible lengths of its sides.

The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing, when the side of the triangle is 20 cm ?

The volume of a spherical balloon is increasing at the rate of 25 cm^(3)//s . Find the rate of change of its surface area at the instant, when its radius is 5 cm.

The surface area of a spherical bubble is increasing at the rate of 2 cm^(2)//s . Find the rate at which the volume of the bubbles is increasing at the instant, when its radius is 6 cm.