The volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex]
The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.
Thus, the volume (V) of a right circular cylinder, using the above formula, is, [tex]V = \pi r^2h[/tex] , where
'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
Given:
Height(h) = 8 x diameter = 16 x radius (r) (diameter = 2 x radius )
∴ h = 16r.
V= [tex]\pi r^2h[/tex]
Substituting h = 16r in the volume formula we get
V = [tex]\pi r^2(16r)[/tex] = [tex]16\pi r^3[/tex]
Thus the volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex].
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