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

Question a:

Mass = Density × Volume
Density = Mass/Volume

Volume of the tree trunk (the shape of Cylinder) = Area of circular base × height
Volume = [πr²] × h
Volume = [π × 0.25²] × 20
Volume = 3.93 m³

Density = 380 kg/m³

Mass = Density × Volume
Mass = 380 × 3.93
Mass = 1493.4 kg

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Question b)

The growth ring = 4 millimeters = 4÷1000 = 0.004
New diameter = 0.5 + 0.004 = 0.5004
New height = 20 + 0.2 = 20.2

New volume = [πr²] × h
New volume = [π × 0.2502²] × 20.2
New volume = 3.97 m³