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A rectangular ribbon of width x is wrapped around the right circular cylinder with radius n shown above, encircling the cylinder without overlap. The area of the ribbon is equal to the area of the base of the cylinder.

Quantity A

Quantity B

x

n

A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

A rectangular ribbon of width x is wrapped around the right circular cylinder with radius n shown above, encircling the cylinder without overlap. The area of the ribbon is equal to the area of the base of the cylinder.

Quantity A

Quantity B

x

n

A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

NICE!!!!

AREA OF RIBBON If we remove the ribbon and lay it flat, we see that it is a rectangle. So, to find the area, we need its length and width. The width = x

The length of the ribbon is equal to the circumference of the cylinder. Circumference = 2(pi)(radius) So, the length = 2(pi)(n)

Area of ribbon = (length)(width) = 2(pi)(n)(x)

----------------------------------------- AREA OF CYLINDER BASE The base is a circle Area of circle = (pi)(radius)² So, area of base = (pi)(n)²

The area of the ribbon is equal to the area of the base of the cylinder. We get: 2(pi)(n)(x) = (pi)(n)² To simplify this, first divide both sides by pi to get: 2(n)(x) = (n)² Next, divide both sides by n to get: 2x = n

Great! We're ask to compare the following: Quantity A: x Quantity B: n

Since 2x = n, we can replace n with 2x to get: Quantity A: x Quantity B: 2x Quantity B is greater.