EXERCISE 7.8

EXERCISE . . Find two positive numbers whose sum is and their product is maximum. .

Find two positive numbers whose product is and their sum is minimum. . Find the smallest possible value of x given that x = . .

A garden is to be laid out in a rectangular area and protected by wire fence. What is the largest possible area of the fenced garden with metres of wire. . A rectangular page is to contain cm of print.

The margins at the top and bottom of the page are . cm and the margins at other sides of the page is cm. What should be the dimensions of the page so that the area of the paper used is minimum. .

A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain , , sq.mtrs in order to provide enough grass for herds. No fencing is needed along the river. What is the length of the minimum needed fencing material?

. Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius cm. . Prove that among all the rectangles of the given perimeter, the square has the maximum area.

. Find the dimensions of the largest rectangle that can be inscribed in a semi circle of radius r cm. . A manufacturer wants to design an open box having a square base and a surface area of sq.cm.

Determine the dimensions of the box for the maximum volume. . The volume of a cylinder is given by the formula V r h = π . Find the greatest and least values of V if r h = .

. A hollow cone with base radius a cm and height b cm is placed on a table. Show that the volume of the largest cylinder that can be hidden underneath is times volume of the cone.