Question

As an oak tree grows taller, it also grows wider. In other

Answer 1

The volume of wood in the tree's trunk as it grows is $16\pi r^3$

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, $V = \pi r^2h$ , 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= $\pi r^2h$

Substituting h = 16r in the volume formula we get

V = $\pi r^2(16r)$ =  $16\pi r^3$

Thus the volume of wood in the tree's trunk as it grows is $16\pi r^3$.

Learn more about volume of a cylinder  here :

brainly.com/question/16134180

#SPJ1