Find the dimensions of the largest rectangle that can be inscribed in a semi circle of radius r cm.

Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10 cm.

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.

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/(3) .

Prove that an angle inscribed in a semi-circle is a right angle using vector method.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) . Also find the maximum volume.

Find the area of the greatest rectangle that can be inscribed in the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1.

Find the magnitude of the linear acceleration of a particle moving in a circle of radius 10 cm with uniform speed completing the circle in 4s.

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 7 cm.