Ratio of the radius of the cone and the height of the cone is 7:9 respectively and the radius of the cone is 50%

Ratio of the radius of the cone and the height of the cone is 7:9 respectively and the radius of the cone is 50% of the radius of the semicircle. If the circumference of the semicircle is 72 cm, then find the volume of the cone?

A. 616 cm3

B. 1232 cm3

C. 462 cm3

D. 1848 cm3

E. None of these

Sol:

Circumference of the semicircle=72 cm

22/7*r+2r=72

r=72*7/36

r=14 cm

Radius of the cone=14/2=7 cm

Height of the cone=7*9/7=9 cm

Volume of the cone=1/3*22/7*7*7*9

=462 cm3