- #1
MHB This is the formula for finding the area of a circle, where r is the radius.
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SUMMARY
The discussion focuses on calculating the area of a circle, specifically a semi-circle, using the formula A = (1/2)(πr²). Participants explore the relationship between the areas of a larger semi-circle and two smaller semi-circles, emphasizing the concept of similarity in geometry. The final area calculation provided is approximately 154 cm² for a semi-circle with a radius of 14 cm. The conversation highlights the importance of clarity in mathematical expressions and the correct application of formulas.
PREREQUISITES- Understanding of basic geometry concepts, particularly circles and semi-circles
- Familiarity with the mathematical constant π (pi)
- Ability to perform basic arithmetic operations, including division and multiplication
- Knowledge of area calculation formulas for circles and semi-circles
- Research the properties of circles and semi-circles in geometry
- Learn about the derivation and applications of the area formula A = πr²
- Explore the concept of similarity in geometric shapes and its implications for area calculations
- Practice solving area problems involving composite shapes, including circles and semi-circles
Students, educators, and anyone interested in mastering geometric calculations, particularly those involving circles and semi-circles.
- #2
I like Serena
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MHB
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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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MHB
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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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MHB
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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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MHB
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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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MHB
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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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