A tree harvester estimates the trunk of a tree to have a height of about 36 meters and a base diameter of about 0.5 meter. The wood of the tree has a density of about 610 kilograms per cubic meter. Find the mass of the trunk. Round your answer to the nearest hundred. in kilograms

Respuesta :

Answer:

The mass of wood is 4309.65 kg.

Step-by-step explanation:

Volume of a cylinder is:

[tex]V = \pi r^{2} h[/tex]

Where [tex]r[/tex] is the radius of base of cylinder

and [tex]h[/tex] is the height of the cylinder

[tex]r=\dfrac{d}{2}[/tex]

[tex]d[/tex] is the diameter of base of cylinder.

A tree's trunk is in the shape of cylinder only. And we are given the following details:

[tex]d = 0.5m\\\Rightarrow r = \dfrac{0.5}{2} m[/tex]

[tex]h =36 m[/tex]

[tex]V = \pi (\dfrac{0.5}{2})^2 \times 36\\\Rightarrow V = 7.065\ m^3[/tex]

Density of wood of tree = 610 kg per cubic meter

Mass of trunk = Volume [tex]\times[/tex] density

[tex]\Rightarrow 610 \times 7.065\\\Rightarrow 4309.65\ kg[/tex]

Hence, mass of trunk is 4309.65 kg.