Q31 of 47 Page 1

A cone of radius 10 cm is divided into two parts by a plane parallel to its base through the mid-point of its height. Compare the volumes of the two parts.


Given: Radius of cone, R = 10cm


To compare: Volumes of two parts


From the figure, we can see that cone is divided into two equal parts by the axis. So,



In ΔAQD and ΔAPC, we have


∠AQD = ∠APC [both are 90°]


∠DAQ = ∠PAC [common]


∴ ΔAQD ~ ΔAPC [by AA similarity criterion]



So, radius


Now, the volume of frustum








Comparing the volume of the frustum and cone





Volume of two parts are in 1 : 7


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