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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