Results 1 to 14 of 14

Math Help - geometry

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    123

    geometry

    These are the MOST hardest questions from my book. Nobody in my class, which is an ADVANCED math honors 11 class, can get them, which is why I'm curious if it's even possible or not.

    If you can answer these questions, you're definitly smarter than my whole class combined.

    I'd like to know why it's that anwer because I'm curious about how to do it.

    I'm clueless as to where to start. Eek!

    1. Given: QR = 12 cm
    <PQR = 30 degrees
    Find: Area of the shaded region

    2. Given: A circle is inscribed in a sector of another circle.
    <A = 60 degrees, AB = 10 sqrt(3) cm

    Find: Shaded area

    3. A spherical tank is filled with water that is 20 ft. deep and 50 ft. wide.

    What is the radius of the tank?

    Note: All these are circles and a cone.
    Attached Thumbnails Attached Thumbnails geometry-mathproj.bmp  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,109
    Thanks
    381
    Awards
    1
    Quote Originally Posted by AlphaRock View Post
    1. Given: QR = 12 cm
    <PQR = 30 degrees
    Find: Area of the shaded region
    Look at the region in two parts, the triangle and the wedge. I presume you can get the area of the wedge. As to the triangle, you know this is an isosceles triangle with a vertex angle of 120 degrees.

    -Dan
    Attached Thumbnails Attached Thumbnails geometry-circle.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by topsquark View Post
    Look at the region in two parts, the triangle and the wedge. I presume you can get the area of the wedge. As to the triangle, you know this is an isosceles triangle with a vertex angle of 120 degrees.

    -Dan
    Unfortunately, I can't.

    However, the closest I got to the answer was 36pie x 60% to get the area of the mid-P-R part of the circle. I can't get the area of the 120 - 30 - 30 one...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,109
    Thanks
    381
    Awards
    1
    Quote Originally Posted by AlphaRock View Post
    Unfortunately, I can't.

    However, the closest I got to the answer was 36pie x 60% to get the area of the mid-P-R part of the circle. I can't get the area of the 120 - 30 - 30 one...
    The central angle of the wedge is 60 degrees so it is 1/6 of the circle. The area of the circle is 36 \pi, so the area of your wedge is 6 \pi.

    For the triangle, see this site.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,109
    Thanks
    381
    Awards
    1
    Quote Originally Posted by AlphaRock View Post
    2. Given: A circle is inscribed in a sector of another circle.
    <A = 60 degrees, AB = 10 sqrt(3) cm

    Find: Shaded area
    What shaded area?

    -Dan
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    May 2008
    Posts
    186
    Quote Originally Posted by topsquark View Post
    What shaded area?

    -Dan
    The arrow
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,109
    Thanks
    381
    Awards
    1
    Quote Originally Posted by AlphaRock View Post
    3. A spherical tank is filled with water that is 20 ft. deep and 50 ft. wide.

    What is the radius of the tank?
    We know that
    25 \cdot 25 = 20 \cdot x

    So
    x = \frac{25^2}{20}

    and we know that 20 + x is a diameter....

    -Dan
    Attached Thumbnails Attached Thumbnails geometry-circle2.jpg  
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by topsquark View Post
    What shaded area?

    -Dan

    Thanks for catching!

    Shaded area for #2 = EVERYTHING OUTSIDE of circle (EVERYTHING NOT IN THE CIRCLE).
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by topsquark View Post
    We know that
    25 \cdot 25 = 20 \cdot x

    So
    x = \frac{25^2}{20}

    and we know that 20 + x is a diameter....

    -Dan
    Thanks, Dan!

    I'm curious. Why is it that 25 * 25 = 20 * x

    I understand what you're saying about how let the rest of the line be x. I'm having a hard time understanding why 25 * 25 = 20 * x. Anybody know?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,109
    Thanks
    381
    Awards
    1
    Quote Originally Posted by AlphaRock View Post
    Thanks, Dan!

    I'm curious. Why is it that 25 * 25 = 20 * x

    I understand what you're saying about how let the rest of the line be x. I'm having a hard time understanding why 25 * 25 = 20 * x. Anybody know?
    This page does a decent job of listing some of the chord theorems. I can't derive them off the top of my head, but maybe someone else will come along an show you how.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by topsquark View Post
    ...I can't derive them off the top of my head, but maybe someone else will come along an show you how.
    Actually you are dealing with a right triangle.

    Let denote a, b and c the sides of the right triangle, p and q the segments of the hypotenuse and h the height of the triangle, then you know:

    p+q=c ....... [1]

    h^2 = a^2-p^2 ....... [2]

    h^2 = b^2-q^2 ....... [3]

    [1] + [2] will yield:

    2h^2 = \underbrace{a^2+b^2}_{c^2}-p^2-q^2

    2h^2 = c^2 - (\underbrace{(p^2+2pq+q^2)}_{c^2} -2pq)

    Thus you have:

    \boxed{h=p \cdot q}
    Attached Thumbnails Attached Thumbnails geometry-euklid_theorem.gif  
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member
    Joined
    Apr 2008
    Posts
    123
    Thanks for your help, guys...

    Is anybody smart enough to do number two (the cone-shape like question)?
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Here's another way to tackle the sphere problem using trig and a Great Circle around the center of the sphere.

    A long chord (width of water surface=50) is given by:

    2Rsin(\frac{\theta}{2})=50...[1]

    The middle ordinate is 20 feet and given by R(1-cos(\frac{\theta}{2}))=20...[2]

    Now, we have two equations with two unknowns and we can solve for R and theta.

    Solve [1] for {\theta}=2sin^{-1}(\frac{25}{r}), sub into [2] and solve for R and we get R=\frac{205}{8}=25.625

    Which agrees with TQ's method.

    It's certainly easier using TQ's method, but if you're interested this is something to know.

    In #2, I can't follow what that cone is supposed to be. Also, someone in advanced honors should know better than to spell {\pi} as 'pie'
    Come on.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by AlphaRock View Post
    ...

    2. Given: A circle is inscribed in a sector of another circle.
    <A = 60 degrees, AB = 10 sqrt(3) cm

    Find: Shaded area

    ...
    I've attached a sketch of the sphere in the cone - as I understand your work of art.

    If I didn't make a mistake you are dealing with 2 equilateral triangles which I have coloured red and green.

    And now it's your turn to show us the shaded region (Copy the sketch into Paint, pour lightgrey paint into the adequate region and upload the modified drawing again)
    Attached Thumbnails Attached Thumbnails geometry-sphere_incone.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Finite Geometry: Young's Geometry
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: September 15th 2010, 07:20 AM
  2. Geometry (1)
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 7th 2009, 06:44 PM
  3. geometry (2)
    Posted in the Geometry Forum
    Replies: 4
    Last Post: November 7th 2009, 06:41 PM
  4. geometry (3)
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 7th 2009, 07:22 AM
  5. Modern Geometry: Taxicab Geometry Problems
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 30th 2009, 07:32 PM

Search Tags


/mathhelpforum @mathhelpforum