Find the largest size of a rectangle that can be inscribed in a semi circle of radius 1 unit, So that two vertices lie on the diameter.

Find the volume of the largest cylinder that can be inscribed in a sphere of radius 'r' cm.

Area of the greatest rectangle that can be inscribed in the ellipse x^2/a^2+y^2/b^2=1 is

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is frac{2R}{sqrt 3} . Also find the maximum volume.

Q.4. Attempt any two of the following: (1) A regular hexagon is inscribed in a circle of radius 14 cm. Find the area of the region between the circle and the hexagon.

Let z_1 be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and z_1 ne pm 1 . Consider an equilateral triangle inscribed in the circle with z_1, z_2, z_3 as the vertices taken in the counter clockwise direction. Then z_1z_2z_3 is equal to

Find the area of the circle if its radius is 2.1 m.

A wire of length 2 units is cut into two parts which are bent respectively to form a square of s i d e=x units and a circle of radius =r units. If the sum of the areas of the square and the circle so formed is minimum, then :