Question

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 D. 25.92 ft3

Answer 1

Answer: 19.54 ft cubed

Explanation:

i took the test and got it right

Answer 2

Option C is correct

`19.54 ft^3`

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  = (4.5)/(2 \pi)`

Substitute in [2] we have;

`V = \pi \cdot ((4.5)/(2 \pi))^2 \cdot 12`

Use
`\pi = 3.14`

⇒
`V= (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`