Question

In the gym there is a round metal pole that is 8 inches in diameter. The gym teacher

wants to wrap the pole tightly with 1-inch thick rope from the ground up to a height of 6 feet.
(The rope will be wound over and over until it reaches a height of 6 feet.) About how much rope
with the gym teacher need? Explain your reasoning.

Answer 1

`1808.64 inches` much rope with the gym teacher need .

Explanation:

Here we have , In the gym there is a round metal pole that is 8 inches in diameter. The gym teacher wants to wrap the pole tightly with 1-inch thick rope from the ground up to a height of 6 feet. (The rope will be wound over and over until it reaches a height of 6 feet.) We need to find About how much rope with the gym teacher need . Let's find out:

According to question , the rope is covered in lateral surface area of a cylinder i.e. to wrap the pole tightly with 1-inch thick rope from the ground up to a height of 6 feet which will cover lateral surface area of cylinder . We know that Formula for lateral surface area is :

⇒
`2\pi r h`

From the question we have

`Radius = (Diameter)/(2) =(8)/(2) =4 inches\\Height = 6 (1feet) = 6(12inches)=72inches`

Now , height of pole is 72 inches and we will wrap pole with 1 inch thick rope , So total number of turns of rope in pole :

⇒
`(72)/(1)`

⇒
`72 Turns`

Now , Length of one turn of rope in pole is equivalent to circumference of circle with radius = 4 inches as:

⇒
`Length = Circumference = 2\pi r`

⇒
`Length = 2\pi (4)`

⇒
`Length =25.12inches`

Since , length of one turn is 25.12 inch so ,length of total rope i.e. of 72 turns is :

⇒
`Length = 72(25.12)`

⇒
`Length = 1808.64inches`

Therefore ,
`1808.64 inches` much rope with the gym teacher need .