A right circular cone with height 10 units is placed inside a hollow right circular cylinder with height 10 units as shown in Figure 1. Water with volume $\mathrm { V } _ { 1 }$ cubic units is poured between this cylinder and cone, and the water height becomes 5 units. Then this object is inverted as shown in Figure 2, and after adding more water, the water volume becomes $\mathrm { V } _ { 2 }$ cubic units and the height becomes 5 units. Accordingly, what is the ratio $\frac { \mathrm { V } _ { 1 } } { \mathrm {~V} _ { 2 } }$? (During this process, water does not enter the cone.) A) $\frac { 3 } { 7 }$ B) $\frac { 5 } { 11 }$ C) $\frac { 8 } { 15 }$ D) $\frac { 10 } { 21 }$ E) $\frac { 15 } { 31 }$
A right circular cone with height 10 units is placed inside a hollow right circular cylinder with height 10 units as shown in Figure 1. Water with volume $\mathrm { V } _ { 1 }$ cubic units is poured between this cylinder and cone, and the water height becomes 5 units. Then this object is inverted as shown in Figure 2, and after adding more water, the water volume becomes $\mathrm { V } _ { 2 }$ cubic units and the height becomes 5 units.
Accordingly, what is the ratio $\frac { \mathrm { V } _ { 1 } } { \mathrm {~V} _ { 2 } }$?
(During this process, water does not enter the cone.)
A) $\frac { 3 } { 7 }$
B) $\frac { 5 } { 11 }$
C) $\frac { 8 } { 15 }$
D) $\frac { 10 } { 21 }$
E) $\frac { 15 } { 31 }$