After years of environmental remediation, a certain region has transformed barren mountains into green mountains and clear waters. To estimate the total timber volume of a certain tree species in a forest area, 10 trees of this species were randomly selected. The cross-sectional area at the base (in $\mathrm { m } ^ { 2 }$ ) and timber volume (in $\mathrm { m } ^ { 3 }$ ) of each tree were measured, yielding the following data:
| Sample number $i$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Total |
| Base cross-sectional area $x _ { i }$ | 0.04 | 0.06 | 0.04 | 0.08 | 0.08 | 0.05 | 0.05 | 0.07 | 0.07 | 0.06 | 0.6 |
| Timber volume $y _ { i }$ | 0.25 | 0.40 | 0.22 | 0.54 | 0.51 | 0.34 | 0.36 | 0.46 | 0.42 | 0.40 | 3.9 |
It is calculated that $\sum _ { i = 1 } ^ { 10 } x _ { i } ^ { 2 } = 0.038 , ~ \sum _ { i = 1 } ^ { 10 } y _ { i } ^ { 2 } = 1.6158 , \sum _ { i = 1 } ^ { 10 } x _ { i } y _ { i } = 0.2474$ .
(1) Estimate the average base cross-sectional area and average timber volume per tree of this species in the forest area;
(2) Find the sample correlation coefficient between the base cross-sectional area and timber volume of this tree species (accurate to 0.01);
(3) The base cross-sectional area of all trees of this species in the forest area was measured, and the total base cross-sectional area of all such trees is $186 \mathrm {~m} ^ { 2 }$ . Given that the timber volume of a tree is approximately proportional to its base cross-sectional area, use the above data to estimate the total timber volume of this tree species in the forest area.
Note: Correlation coefficient $r = \frac { \sum _ { i = 1 } ^ { n } \left( x _ { i } - \bar { x } \right) \left( y _ { i } - \bar { y } \right) } { \sqrt { \sum _ { i = 1 } ^ { n } \left( x _ { i } - \bar { x } \right) ^ { 2 } \sum _ { i = 1 } ^ { n } \left( y _ { i } - \bar { y } \right) ^ { 2 } } } , \sqrt { 1.896 } \approx 1.377$ .