An architect wants an artistic flair to the house he is building, so he designs windows that are three fourths of a circle in sh

Question

2 years ago

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An architect wants an artistic flair to the house he is building, so he designs windows that are three fourths of a circle in sh

ape. The builder is making trim for the windows and needs to know the length of the arc of the outer rim of the window. If the central angle is 270 degrees, and the radius of the partial circle is 30 inches, how much trim is needed for each window? Round your answer to the nearest inch, and enter the number only.

Mathematics

1 answer:

larisa86 [58] · Answer 1 · 2023-08-08T14:48:55+03:00

The amount of rim needed for each window is 141.4 in

<h3>How to find the length of the outer rim?</h3>

Since the outer rim is the length of an arc, we use the formula for length of an arc of a circle.

An arc is part of section of the circumference of a circle

<h3>What is the length of an arc?</h3>

So, length of arc, L = Ф/360 × 2πR where

Ф = central angle of arc and
R = radius of circle.

Gven that for the window rim

Ф = angle of the rim = 270° and
R = radius of the rim = 30 in

Substituting the values of the variables into the equation for L, we have

L = Ф/360 × 2πR

L = 270°/360° × 2π × 30 in

L = 3/4 × 2π × 30 in

L = 3/2 × π × 30 in

L = 3 × π × 15 in

L = 45π in

L = 141.37 in

L ≅ 141.4 in

So, the amount of rim needed for each window is 141.4 in

Learn more about length of an arc here:

brainly.com/question/8402454

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