A cone of height h cm and base radius r cm is made from a spherical solid of radius 10cm. Show that #r^2=20h-h^2#.?

1 Answer
P dilip_k
Apr 3, 2018

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A cone ABC of height #AD= h cm# and base of radius #CD= r cm # is made from a spherical solid of radius # OA=OB=OC= 10cm#, where #O# is the center of the sphere.

We are to show that #r^2=20h-h^2#.

For right #Delta ODC,angle ODC=90^@#

So by Pythagoras theorem we have

#OC^2=OD^2+CD^2#

#=>10^2=(h-10)^2+r^2#

#=>10^2=h^2-20h+10^2+r^2#

#=>r^2=20h-h^2#

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