Question

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.

Answer 1

Tree is not suitable for tapping .

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

⇒
`4.166667 = 2\pi r`

Use
`\pi =3.14`

⇒
`4.166667 = 2*3.14* r`

⇒
`4.166667 = 6.28 * r`

⇒
`r=(4.166667)/(6.28)`

⇒
`r=0.663482006`

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 .

Answer 2

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.