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Thread: Area and Circumference, homework for 2moro!

  1. #1
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    Area and Circumference, homework for 2moro!

    Hello, please can you help me solve these math problems i am having some trouble.
    Q1. a circle has an area of 98mm(squared).
    Calculate the circumference of the circle.

    The picture for question 2 is attached to this message sorry about the bad drawing.

    Q2. Calculate the shade area

    I really appreciate anyone who can help me with this thanks in advance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sammyfox07 View Post
    Hello, please can you help me solve these math problems i am having some trouble.
    Q1. a circle has an area of 98mm(squared).
    Calculate the circumference of the circle.
    The area of a circle is $\displaystyle A=\pi r^2$, so in this case we have:

    $\displaystyle A=\pi r^2=98$ so $\displaystyle r=\sqrt{98/\pi}$

    The circumference of a circle is $\displaystyle C=2 \pi r$, so in this case we have:

    $\displaystyle
    C=2 \pi r=2 \pi \sqrt{98/\pi}=2 \sqrt{98 \pi}=14 \sqrt{2 \pi} \rm{\ mm}
    $

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by sammyfox07 View Post
    The picture for question 2 is attached to this message sorry about the bad drawing.

    Q2. Calculate the shade area

    I really appreciate anyone who can help me with this thanks in advance.
    I assume the shaded areais the area left in a square of side 12 cm when 4 quarter circles of radius 6 cm are removed from the corners.

    So the shaded area is the difference between the area of the square and that
    of a circle of radius 6 cm.

    $\displaystyle A=12^2-\pi 6^2 \rm{\ cm^2}$

    RonL
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  4. #4
    Member Jonboy's Avatar
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    Q1. a circle has an area of 98mm(squared).
    Calculate the circumference of the circle.
    If you want baby steps... read here:

    Can you solve a system of equations? That's what this method is going to be.

    So the area of a circle is: $\displaystyle \pi r^2$

    Then we know: [1] $\displaystyle 98 = \pi r^2$

    The circumference of a circle is: [2] $\displaystyle \pi 2r$

    So to find the circumference, we need to know the r.

    So we solve equation [1] for r: $\displaystyle \frac{98}{\pi} = r^2 \Rightarrow r = \frac{7\sqrt{2}}{\sqrt{\pi}}$

    Now you have r, so solve [2] by subbing our new r value in the equation:

    $\displaystyle \pi 2\frac{7\sqrt{2}}{\sqrt{\pi}} = \frac{14\pi \sqrt{2}}{\sqrt{\pi}}$

    We're not allowed to have a sqrt on the bottom, so we multiply the top and bottom by $\displaystyle \sqrt{\pi}$:

    $\displaystyle \frac{14\pi\sqrt{2\pi}}{\pi} = \boxed{\frac{14}{\sqrt{2\pi}}\,mm}$
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