If circumference C is given
Diameter D = C/pi
Where pi=3.14
Since C is 4 feet and 2 inches or 4.1667 feet
Diameter then is equal to 1.327 feet
Required diameter for tapping is 1.5 feet, therefore, the maple tree measure is not yet suitable.
Answer:
Tree is not suitable for tapping .
Step-by-step explanation:
Given :
Maple trees suitable for tapping for syrup should be at least 1.5 feet in diameter
You wrap a rope around a tree trunk, then measure the length of the rope needed to wrap one time around the trunk. this length is 4 feet 2 inches.
To Find : Explain how we can use this length to determine whether the tree is suitable for tapping.
Solution :
Since we are given that length of rope needed to wrap one time around the trunk = 4 feet 2 inches.
Thus, The circumference of tree is 4 feet 2 inches.
Convert the unit of circumference in feet .
1 inches = 0.0833333 foot
2 inches = 0.0833333*2 =0.166667
Thus, 4 feet 2 inches. = 4.166667 feet
Now to calculate diameter Use Circumference formula :
Circumference = 2πr
⇒[tex]4.166667 = 2\pi r[/tex]
Use [tex]\pi =3.14[/tex]
⇒[tex]4.166667 = 2*3.14* r[/tex]
⇒[tex]4.166667 = 6.28 * r[/tex]
⇒[tex]r=\frac{4.166667}{6.28}[/tex]
⇒[tex]r=0.663482006[/tex]
Thus Radius is 0.663482006 feet
Since Diameter = 2 * Radius
⇒Diameter = 2 * 0.663482006
⇒Diameter = 1.32696401 feet
Since we are given that the diameter should be at least 1.5 feet .
And our calculated diameter 1.32696401 feet is less than the given diameter 1.5 feet.
Hence , Tree is not suitable for tapping .
