The radius and slant hight ofa cone are in the ratio of 4:7. its Curved Surface Area is #352 cm^2#. find the volume of cone ?

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Answer 1 · 2018-03-12T12:38:04

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Let the radius and slant height of the cone be #r# and #l# respectively.

So by the given condition we have

#r/l=4/7.......[1]#

Now Curved Surface Area of the cone #352cm^2#

So we get

#pirl=352#

#rl=352xx7/22=112......[2]#

Multiplying [1] and [2] we get

#r/lxxrl=4/7xx112#

#=>r^2=64=8^2#

#=>r=8# cm

Inserting in [2] we get

#8l=112#

#=>l=112/8=14# cm

So height of the cone

#h=sqrt(l^2-r^2)=sqrt(14^2-8^2)=sqrt132=2sqrt33#cm

Volume of the cone

#V=1/3pir^2h#

#=>V=1/3*pi*8^2*2sqrt33~~770cm^3#