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.

 much rope  with the gym teacher need .

Step-by-step 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 :

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From the question we have

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 :

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

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

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Therefore ,  much rope  with the gym teacher need .

i think the correct option is the second option.