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

Find the area of a circle of radius r, by integration.

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.

Let ABCbe an isosceles triangle inscribed ina circle having radius r. Then by figure area of the triangle ABC is triangle Find (d triangle)/(d theta) and (d^2 triangle)/(d theta^2) .

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 .

A right circular cylinder is inscribed in a given cone of radius R cm and height H cm as shown in the figure. Find a relation connecting x and R when S is a maximum.

A right circular cylinder is inscribed in a given cone of radius R cm and height H cm as shown in the figure. Find the Surface area S of the circular cylinder as a function of x.

A window is in the form of a rectangle surmounted by a semicircle as shown in the figure. If r is the radius of the semicircle and x is the length of the larger side of the rectangleThe perimeter of the window is 5 metres Find the area of the window in terms of r.

A rectangle of area seven square centimetres is cut into three equal : rectangles. What is the area of each? ii) What if it were cut into four?