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. explain how you can use this length to determine whether the tree is suitable for tapping.

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. 

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

⇒

Use

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⇒

⇒

⇒

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 .