toy treasures - arvind gupta (60 kb doc)

SURFACE OF A SPHEREHere is a very simple and practical wayto prove that “the surface area of asphere is equal to four times the surfacearea of the circle through its center.”In other words when you cut a lemoninto half, the size of one of its flat faces isone quarter of the area of the wholefruit.Take an old ball and carefully cut it intotwo equal halves.Fill the two halves with clay and letthem dry.Take one of the half circle sections anddrive a nail into its upper most pointFig (1).Attach one end of a cord to the nail andcurl the rope around it spiralingoutward in ever-increasing rings.When the entire circle is covered cut thecord and put it aside Fig (3).Drive a nail into the center of the flatsurface of the other half-sphere Fig (2).Use the same size rope as before and coilit around the nail until the entire surfacearea is covered Fig (4).Unroll and measure the two lengths ofcord you now have.The first will be exactly twice the lengthof the second.But as it is only half the surface of theentire sphere, we can conclude that it isactually four times as great as the other,the circle through the center.