- #1
This is the formula for finding the area of a circle, where r is the radius.
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Discussion Overview
The discussion revolves around finding the area of a circle, specifically in the context of a problem involving a larger semicircle from which two smaller semicircles are removed. Participants explore various approaches and reasoning related to this geometric problem.
Discussion Character
- Exploratory
- Mathematical reasoning
- Homework-related
Main Points Raised
- One participant seeks assistance in calculating the area of a circle, describing a configuration involving a large semicircle and two smaller semicircles.
- Another participant suggests using the concept of similarity to determine the areas of the smaller semicircles, noting that their areas are one-fourth that of the larger semicircle.
- A different participant points out that the area of the semicircle has been found, but there was confusion regarding the division by two, suggesting clarity in the use of the equal sign.
- One participant questions the simplicity of the calculation, while another asserts that finding half the area of a semicircle is indeed straightforward.
- A participant presents a calculation for the area, approximating it to 154 cm², and seeks confirmation of its accuracy.
- Another participant provides a formula for the area, expressing it in terms of π and the radius, and approximates the area to 154 cm² as well.
Areas of Agreement / Disagreement
Participants express varying levels of understanding and approaches to the problem, with no consensus reached on the best method or clarity of the calculations. Some participants agree on the area approximations, while others highlight confusion in the reasoning.
Contextual Notes
There are indications of confusion regarding the division of areas and the clarity of the problem statement. The discussion reflects different interpretations of the geometric configuration and the calculations involved.
- #2
I like Serena
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susanto3311 said:
Hey! ;)
It looks like a big half circle from which 2 smaller half circles are removed.
Let's start with those.
Can you tell what their radius's are? (Wondering)
- #3
MarkFL
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Another approach would be to utilize the concept of similarity. The two smaller semi-circles have linear measures that are one-half that of the corresponding measures of the larger semi-circle, so we know their areas must each be one-fourth that of the larger. Since there are two of them, we then know the combined areas of the two smaller semicircles is one half that of the larger. So, find the area of the larger, and cut it in half (divide by two) and you will have the area in question. :D
- #4
- #5
MarkFL
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You want to find half of the area of the semi-circle...it appears you have found the area of the semi-circle...
edit: nevermind...it was unclear at first that you have divided by 2 twice...you should only use the equal sign to equate 2 quantities that are equal. :D
edit: nevermind...it was unclear at first that you have divided by 2 twice...you should only use the equal sign to equate 2 quantities that are equal. :D
- #6
susanto3311
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could you make more simple?...
- #7
MarkFL
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More simple than finding half the area of a semi-circle? No. :D
- #8
susanto3311
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how about...
= 308/2 = 154 cm2
it's true...??
= 308/2 = 154 cm2
it's true...??
- #9
MarkFL
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I would write:
$$A=\frac{1}{2}\left(\frac{\pi}{2}(14\text{ cm})^2\right)=49\pi\text{ cm}^2\approx154\text{ cm}^2$$
$$A=\frac{1}{2}\left(\frac{\pi}{2}(14\text{ cm})^2\right)=49\pi\text{ cm}^2\approx154\text{ cm}^2$$
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