12 . In the figure , a right inverted circular cone of radius r is inscribed in a sphere with centre O and fixed radius R . The perpendicular height of the cone is h , where 0� r � R � h � 2R
. P is the centre of its circular base where its circumference touches the sphere .
R
P O h r
Let V be the volume of the circular cone .
( a ) Express V in terms of � , R and h .
( b ) Hence , show that
R � � � 2�h
.
2 2 ( c ) Show that V attains its maximum when r � R.
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( d ) Hence , write down the maximum value of V , giving the answer in the form
3 a� R .
16 ( e ) Is the curved surface area of the circular cone greater than � R
9 when its volume attains its maximum ? Explain your answer .
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