Originally,
h = 20 m, the height of the tree trunk
d = 0.5 m, the diameter of the trunk
Because the density is 380 kg/m³, the mass of the trunk is
[tex]m= \frac{ \pi }{4} (0.5 \, m)^{2}(20 \, m)(380 \, \frac{kg}{m^{3}} ) = 1492.3 \, kg[/tex]
Answer: 1492.3 kg
After one year:
After the tree puts on a growth ring, the new diameter is
d = 0.5 + 2(4 x 10⁻³ m) = 0.508 m
The tree grows by 0.2 m, s the new height is
h = 20 + 0.2 = 20.2 m
The increase in volume is
[tex]\Delta V= \frac{ \pi }{4} (0.508 \, m)^{2}(20.2 \, m) - \frac{ \pi }{4} (0.5 \, m)^{2}(20 \, m) = 0.1672\, m^{3}[/tex]
Answer: The volume produced is 0.17 m³ (nearest hundredth)
