Question

The c.s.a. of a cone is 1159 5/7cm2.area of its base is 254 4/7cm2.find its volume

Answer 1

 c.s.a of cone is pirl. it is given c.s.a is 8118/7 and its base is 1782/7.
 first we have to find area of the circle which is base of cone 
area of cone is pir^2 
so 22/7 x r^2 = 1782/7
r^2 = 1782/7 x  7/22 
r^2 = 1782/22 = 81
r= root 81 
r=9
now we have got radius so now we have to calculate volume 
volume of cone is 1/3pir^2h
here we dont know h to find h we have to simplify c.s.a which it was given
c.s.a pirl=8118/7
22/7 x 9 x l = 8118/7
l = 8118/7 x 7/22 x 1/9
l= 902/22= 41
hence we find l value now we have to find volume
1/3pir^2h
to calculate h we know that slant height formula l^2 = h^2 + r^2
41^2 = h^2 + 9^2 
1681= h^2+81
1681-81=h^2
1600=h^2
root 1600=h
40=h
volume 1/3pir^2h
1/3 x 22/7 x 9 x 9 x 40
= 3394.28
volume of cone is 3394.28