Geometry!!

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#HelpMe!

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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`bold` or `__bold__`	bold
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1. numbered 2. list	numbered list
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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

the answer is 3π/16

ANSHUL CHAUHAN - 8 years, 2 months ago

4a1 + 4π(1/4)^2 - 4a2 = π(1)^2

ANSHUL CHAUHAN - 8 years, 2 months ago

$4a_1+4π(1/2)^2 - 4a_2 = π(1)^2$ , implies $a_1 - a_2 = 0$

Adam Silvernail - 8 years, 2 months ago

Dharmik Panchal - 8 years, 2 months ago

Everyone has assumed that a1 and area of other "similar looking" sectors are equal, so that 4a1 is their total area. Similar assumption have been made for a2 also. But one needs to prove these assumptions.

Shubham Srivastava - 8 years, 2 months ago

Here is the another method. Though the answer is same but the reasoning involved in this method is such that one doesn't require the above stated two assumptions, so there is no need to prove the assumptions. $Area Of Sector SOQ = \frac {90}{360} \pi r^2$ $Area Of Semicircle STO = \frac {1}{2} \pi (\frac {r}{2})^2 = Area Of Semicircle QTO$ $Sector SOQ = a_1 + Semicircle STO + Semicircle QTO - a_2$ $\frac {1}{4} \pi r^2 = a_1 - a_2 + 2 \times (\frac {1}{2} \pi \frac {r^2}{4})$ $a_1 - a_2 = \frac {1}{4} \pi r^2 - \frac {1}{4} \pi r^2 = 0$

Shubham Srivastava - 8 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$