Mathematics

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

1 Answer

  • Answer:

    Option C is correct

    [tex]19.54 ft^3[/tex]

    Step-by-step 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]

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