In Predicting the Growth of the Volume of a Small $\sqrt [ 3 ] { \widehat { volume} } = 2.34 + 4.56$

In predicting the growth of the volume of a small bay by measuring the height of the water at a dock, a researcher is using a model of $\sqrt [ 3 ] { \widehat { volume} } = 2.34 + 4.56$ (height) where height is measured in $\mathrm { m }$ and volume cubic miles. If the height rises to $3.45 \mathrm {~m}$ , what is the predicted volume?

A) $2.62 \mathrm {~m} ^ { 3 }$
B) $1.2 \times 10 ^ { 12 } \mathrm {~m} ^ { 3 }$
C) $5902 \mathrm {~m} ^ { 3 }$
D) $7 \times 10 ^ { 7 } \mathrm {~m} ^ { 3 }$
E) $18.1 \mathrm {~m} ^ { 3 }$