Question

The height of a tree trunk is 20 meters and the base diameter is 0.5 meter. a. The wood has a density of 380 kilograms per cubic meter. Find the mass of the trunk to the nearest kilogram. The mass of the tree trunk is about kilograms. Question 2 b. The trunk puts on a growth ring of 4 millimeters and its height increases by 0.2 meter this year. How many cubic meters of wood does the tree trunk produce? Round your answer to the nearest hundredth. The tree trunk produces about cubic meters of wood this year.

Answer 1

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
$m= \frac{ \pi }{4} (0.5 \, m)^{2}(20 \, m)(380 \, \frac{kg}{m^{3}} ) = 1492.3 \, kg$

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
$\Delta V= \frac{ \pi }{4} (0.508 \, m)^{2}(20.2 \, m) - \frac{ \pi }{4} (0.5 \, m)^{2}(20 \, m) = 0.1672\, m^{3}$

Answer: The volume produced  is 0.17 m³ (nearest hundredth)