Let us say the sum of perimeter of square and circumference of circle be L
Given sum of the perimeters of a square and a circle.
Assuming, side of square = a and radius of circle = r
Then, L = 4a + 2πr
= a = \( \dfrac{ (L – 2πr)}{4}\)… (1)
Let the sum of area of square and circle be S
So, S = a2 + πr2
A wire of length 20 m is to be cut into two pieces. One of the pieces will be bent into shape of a square and the other into shape of an equilateral triangle. Where the wire should be cut so that the sum of the areas of the square and triangle is minimum?
A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces so that the combined area of the circle and the square is minimum?
Of all the closed cylindrical cans (right circular), which enclose a given volume of 100 cm3, which has the minimum surface area?
Divide 15 into two parts such that the square of one multiplied with the cube of the other is minimum.
How should we choose two numbers, each greater than or equal to –2, whose sum is \( \dfrac{1}{2}\) so that the sum of the first and the cube of the second is minimum?