Answer:
Option C is correct
\(19.54 ft^3\)
Step-by-step explanation:
Assume that the truck is in cylindrical shape with uniform circumference.
Circumference(C) of the trunk is given by:
\(C = 2 \pi r\) .....[1]
where, r is the radius of the trunk.
Volume of the cylinder(V) is given by:
\(V = \pi r^2h\) .....[2]
where, r is the radius and h is the height of the tree trunk.
As per the statement:
If the trunk is 12 feet tall with a circumference of 4.5 feet
⇒ h = 12 feet and C = 4.5 feet
From equation [1], we have;
\(4.5 = 2 \pi r\)
Divide both sides by \(2 \pi\)
\(r = \frac{4.5}{2 \pi}\)
Substitute in [2] we have;
\(V = \pi \cdot (\frac{4.5}{2 \pi})^2 \cdot 12\)
Use \(\pi = 3.14\)
⇒\(V= \frac{12 \cdot 4.5 \cdot 4.5}{4 \cdot 3.14}\)
Simplify:
\(V \approx 19.54 ft^3\)
Therefore, the approximate volume of a tree trunk is, \(19.54 ft^3\)