12. A solid right cone and a solid hemisphere have the same base. The

1.	12. A solid right cone and a solid hemisphere have the same base. The volume of the cone is doublehat of the hemisphere. Find the ratio of the height of the cone and the diameter of theemisphere.3) 2:14)3:1
Answer» Volume of hemisphere=2/3pir^3Volume of right cone = 1/3pihr^2 2Vh = Vc(Vh = volume hemisphere, Vc = volume cone) 4/3pir^3=1/3pihr^2multiply by 3 4pir^3=pihr^2 If they have the same base, their radii are the same. dividing both sides by pir^2 yields 4r=h 2r=diameter, so r=d/2 4d/2=h 2d=hhence ratio is 1:2

12. A solid right cone and a solid hemisphere have the same base. The volume of the cone is doublehat of the hemisphere. Find the ratio of the height of the cone and the diameter of theemisphere.3) 2:14)3:1

Answer»

Volume of hemisphere=2/3*pi*r^3Volume of right cone = 1/3*pi*h*r^2

2Vh = Vc(Vh = volume hemisphere, Vc = volume cone)

4/3*pi*r^3=1/3*pi*h*r^2multiply by 3

4pi*r^3=pi*h*r^2

If they have the same base, their radii are the same. dividing both sides by pi*r^2 yields

4*r=h

2r=diameter, so r=d/2

4*d/2=h

2d=hhence ratio is 1:2