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 .

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

srry ask agian

step-by-step explanation: