The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

Given the sum of the perimiter of a square and a circle, show that the sum of their areas is least when the side of the square is equal to radius of the circle.

A farmer wants to construct a circular well and a square garden in his field. He wants to keep sum of their permeters fixed. The prove that the sum of their area is least when the side of a square garden is double the radius of the circular well. Do you think good planning can save energy, time and money.

State whether true or false. If the side of the square is doubled then its area is also doubled.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

The diameters of two circles are in the ratio of 4 : 3and the sum of the their areas is equal to the area of the circle, whose radius is 5 cm. Find the diameters of the two circles.

The sum of the surface areas of a rectangualr parallelopiped with sides x, 2 x and x/3 and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if x is equal to three times the radius of the sphere. Also find the minimum value of the sum of their volumes.

If d varies directly as t^(2) then dt^(2)=k where k is some constant ?

If the area of a circle increases at a uniform rate, then prove that the perimeter varies inversely as the radius.

A square is made inside the circle. Find the area of that portion of the circle which is not inside the square, if the radius of the circle is 10 cm. ( pi = 3.14 )