a cone of radius 10cm is divided into two parts by a plane parallel to its base through the midpoint of its height compare the vlues of the two parts
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In such case the ratio of the volumes of each part can be calculated as follows:
Here, AG = GH = h
And since triangle AGD ~ triangle AHC ( by AAA similarity criterion)
So, (AG/AH) = (GD / HC) ( corresponding sides of similar triangles)
=> h/ 2h = GD /10
=> 2GD = 10
=> GD = 5 cm
So, now, Volume of Cone AED = 1/3 pi r² h
=> 1/3 pi * 25 * h …………(1)
And Volume of the frustum BCDE Of the Cone = Volm (Cone ABC) — Volm ( ConeAED)
= 1/3 * pi* 100* 2h — 1/3 * pi* 25*h
= 1/3* pi* h ( 200 - 25)
= 1/3 * pi * h* 175 ………….(2)
So ratio of 2 parts = (1) ÷ (2)
=> (1/3*pi*25*h) ÷( 1/3*pi*h*175)
= 25/175
= 1/7
So, the volume of the frustum is 7 times the volume of the smaller upper cone.