Question

Alan needs to manufacture a circular metal plate with a perimeter of `10pi` centimeters. If the allowed error tolerance in the perimeter is `+-1` centimeter, how close to the ideal radius must he control the radius of the plate?
A. `1/(5pi)`
B. `1/(10pi)`
C. `2/pi`
D. `1/(2pi)`

Answer: D. `1/(2pi)`

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Answer 1

The ideal radius Alan must control is $\frac{1}{2\pi }$ cm.

Define perimeter of circle.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The area of a circle determines the space it takes up. A circle's diameter is equal to the length of a straight line traced through its center. Usually, it is stated in terms of units like cm or m.

Given data -

Perimeter of circular plate = 10$\pi$ cm

We know that perimeter of a circle is 2$\pi$r

Therefore   10$\pi$ = 2$\pi$r

r = 5 cm

The given error Alan can make is +-1 cm.

Minimum radius is given by

2$\pi$r = 10$\pi$ - 1

r = $\frac{10\pi - 1 }{2\pi }$

r = 5 - $\frac{1}{2\pi }$

Maximum radius is given by

2$\pi$r = 10$\pi$ + 1

r = $\frac{10\pi + 1 }{2\pi }$

r = 5 + $\frac{1}{2\pi }$

The ideal radius Alan must control is $\frac{1}{2\pi }$ cm.

To know more about perimeter of circle, visit:

brainly.com/question/2718232

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