If the radius of the octahedral void is 'r' and radius of the atoms in close-packing is 'R', derive relation between'r' and 'R'.

A window is in the form of a rectangle surmounted by a semicircle as shown in the figure. The perimeter of the window is 5 metres. If r is the radius of the semicircle and x is the length of the larger side of the rectangle, find a relation between r,x.

Prove that if the hypotenuse of a right triangle is 'h' and the radius of its incircle is 'r', then its area is 'r(h+r)'

Assertion : A tetrahedral void is surrounded by four spheres and an octahedral void is surrounded by six spheres. Reason : In hcp or ccp the number of tetrahedral voids is double the number of close packed spheres and number of octahedral voids is equal to number of close packed spheres.

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