Show that the height of the cylinder of maximum volume that can
be inscribed in a sphere of radius is `(2R)/sqrt3`. Also find the
maximum volume.

Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of the sphere.

The length of the longest size rectangel of maximum area that can be inscribed in a semicircle of radius 1, so that 2 vertices lie on the diameter, is a) sqrt2 b)2 c) sqrt3 d) (sqrt2)/(3)

What is the volume of the cone of maximum size that can be carved from a cube of edge 12 centimetres?

Rectangles are inscribed inside a semi-circle of radius r. Find the rectangle with maximum area.

Let x and y be the length and bredth of the rectangle ABCD in a circle having radius r. Let angleCAB=theta (Ref. Figure). If triangle represent area of the rectangle and r is a constant. Show that the rectangle of maximum area that can be inscribed in a circle of radius r is a square of side sqrt2r .

Prove that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 rd the diameter of the sphere.

Calculate the surface area and volume of a sphere of radius '3 cm .'

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 times the radius of the base.