SOLUTION: the ratio of the volume to the area of the right circularcone is 3:1, if the altitude is 12cm. what is the volume of the right circular cone?

Question 866306: the ratio of the volume to the area of the right circularcone is 3:1, if the altitude is 12cm. what is the volume of the right circular cone?
Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
the ratio of the volume to the area of the right circularcone is 3:1, if the altitude is 12cm. what is the volume of the right circular cone?
Answer volume of cone =1/3 pie r^2 h
area of cone =pie r l
ratio of volume : area =3:1
1/3 pie r^2 h :pie r l =3:1
r h/3l = 3/1 (by cross multiplication)
9l = rh squaring both side
81l^2=r^2 h^2 ( we know l^2=r^2+h^2)
81(r^2+h^2)=r^2 h^2 given than h=12
81(r^2+12^2)= r^2 x 12^2
81 r^2 + 81 x 144= 144 r^2
11664 = 144 r^2-81 r^2
1296= 63 r^2
r^2=11664/63
r^2=185.14
volume =1/3 x 22/7 x r^2 x 12 by putting the value of r^2 = 185.14
volume =1/3 x 22/7 x 185.14 x 12= 1 x 22 x 185.14 x 12/3 x 7 =
48876.96/21=2327.47 cubic cm

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