What is the approximate volume of a tree trunk if the trunk is 12 feet tall with a circumference of 4.5 feet? A. 29.40 ft3 B. 21.17 ft3 C. 19.54 ft3
Question
1 Answer

1. User Answers OrethaWilkison
Answer:
Option C is correct
[tex]19.54 ft^3[/tex]
Stepbystep explanation:
Assume that the truck is in cylindrical shape with uniform circumference.
Circumference(C) of the trunk is given by:
[tex]C = 2 \pi r[/tex] .....[1]
where, r is the radius of the trunk.
Volume of the cylinder(V) is given by:
[tex]V = \pi r^2h[/tex] .....[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;
[tex]4.5 = 2 \pi r[/tex]
Divide both sides by [tex]2 \pi[/tex]
[tex]r = \frac{4.5}{2 \pi}[/tex]
Substitute in [2] we have;
[tex]V = \pi \cdot (\frac{4.5}{2 \pi})^2 \cdot 12[/tex]
Use [tex]\pi = 3.14[/tex]
⇒[tex]V= \frac{12 \cdot 4.5 \cdot 4.5}{4 \cdot 3.14}[/tex]
Simplify:
[tex]V \approx 19.54 ft^3[/tex]
Therefore, the approximate volume of a tree trunk is, [tex]19.54 ft^3[/tex]