Results 1 to 12 of 12

Math Help - Some word problems. Please help!

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    6

    Question Some word problems. Please help!

    Hi there, first post on these forums. So i require assistance for a couple of word problems and would greatly appreciate the help.

    1)
    A wheel is spinning at a rate of 220 rad/sec. Find the linear speed of a point on the rim, if the wheel's diameter is 1.5 meters.

    2)
    For a circle of radius 30 meters, find the area (to the nearest m^2) of a sector with a central angle of 120degrees.

    3)
    A flower garden is a 270degree sector with a radius of 4 meters. Find the exact area of the garden (in terms of pi), and approximate to 1 decimal place.

    Thank you all in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Do you have any attempts of finding solutions to supplement these questions?

    Have you researched which formulas may help?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    6
    for question number 2, area of a circle is piR^2. by that, i simply converted the pi into 120/360 (since pi = 360) and then proceeded to find the area with the following equation:
    120/360 x 30^2

    answer wasnt correct.

    For question 3, i converted 270deg into radians....3pi/2
    by the same formula as above....piR^2, i did the following:
    3pi/2 x 1/pi x 4^2

    answer wasnt correct.

    question one, i had no idea how to do it. Velocity is m/s but i have no idea how to cancel out the rad
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by niCe99 View Post
    i simply converted the pi into 120/360 (since pi = 360)
    Not sure who told you that!

    Try, A_{sector} =\frac{\theta}{360}\times \pi r^2 =  \frac{120}{360}\times \pi \times 30^2
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member eumyang's Avatar
    Joined
    Jan 2010
    Posts
    278
    Thanks
    1
    Quote Originally Posted by niCe99 View Post
    1)
    A wheel is spinning at a rate of 220 rad/sec. Find the linear speed of a point on the rim, if the wheel's diameter is 1.5 meters.
    The wheel's radius is 0.75 m, which means that the length of the intersected arc for an angle of 1 radian is 0.75 m. So
    \frac{220 \,\text{rad}}{1 \,\text{sec}} \times \frac{0.75 \,\text{m}}{1 \,\text{rad}}
    would give you the linear speed in m/sec.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jul 2010
    Posts
    6
    Quote Originally Posted by pickslides View Post
    Not sure who told you that!

    Try, A_{sector} =\frac{\theta}{360}\times \pi r^2 =  \frac{120}{360}\times \pi \times 30^2

    Amazing!

    thank you so much
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2010
    Posts
    6
    Quote Originally Posted by eumyang View Post
    The wheel's radius is 0.75 m, which means that the length of the intersected arc for an angle of 1 radian is 0.75 m. So
    \frac{220 \,\text{rad}}{1 \,\text{sec}} \times \frac{0.75 \,\text{m}}{1 \,\text{rad}}
    would give you the linear speed in m/sec.
    so 1 rad is proportional to the radius of the circle? always?

    thanks
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,865
    Thanks
    640
    Quote Originally Posted by niCe99 View Post
    so 1 rad is proportional to the radius of the circle? always?

    thanks
    the basic formula for linear speed is v = r\omega , where v is the linear speed in m/s and \omega is the angular speed in rad/sec
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member eumyang's Avatar
    Joined
    Jan 2010
    Posts
    278
    Thanks
    1
    A radian is an angle measure such that if you look at the intercepting arc on the circle, that length would be the same length as the radius. So in the problem, the wheel's radius was 5 m instead, you would set up the multiplication like this:
    \frac{220 \,\text{rad}}{1 \,\text{sec}} \times \frac{5 \,\text{m}}{1  \,\text{rad}}
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Jul 2010
    Posts
    6
    Quote Originally Posted by eumyang View Post
    A radian is an angle measure such that if you look at the intercepting arc on the circle, that length would be the same length as the radius. So in the problem, the wheel's radius was 5 m instead, you would set up the multiplication like this:
    \frac{220 \,\text{rad}}{1 \,\text{sec}} \times \frac{5 \,\text{m}}{1  \,\text{rad}}
    how does traditional radians, such as pi/2, pi/3, pi/4 ect, in the unit circle get classified? the radius of a unit circle is 1 so....would it just be 1 x whatever radian it is?....so like 1 x pi/3.

    oh is that why you would multiple 5m/1rad with 220rad/sec? since we have the radian...

    sorry. i have NEVER taken a trigonometry class before (they didnt teach it in high school for some reason) and i am doing first year calc and getting my butt kicked from the trigonometry portion of it. In essence, i have had about 8 hours (2 weeks) worth of trigonometry lessons. I learned the basic sin, cos, tan as well as identities and very very vague amount on the unit circles of radians (for what its worth, my teacher is not doing a very good job at teaching trig even though he said he would teach it to us as if we have never seen trig before. I had to self-learn myself but am limited to the resources and TIME, other courses, that i have). We are already up to the calculus portion of trig and thats seems to be alot easier for me anyways.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Senior Member eumyang's Avatar
    Joined
    Jan 2010
    Posts
    278
    Thanks
    1
    Quote Originally Posted by niCe99 View Post
    how does traditional radians, such as pi/2, pi/3, pi/4 ect, in the unit circle get classified? the radius of a unit circle is 1 so....would it just be 1 x whatever radian it is?....so like 1 x pi/3.
    The formula to find the circumference of a circle with radius r is 2πr, so a circle with radius of 1 m would have a circumference of 2π m. And it's 360° around the circle, so you have the relationship that 360° = 2π rad. Half way around the circle is 180°, and half of 2π rad is π rad. So 180° = π rad.

    To convert an angle measurement from degrees to radians multiply by
    \frac{\pi \,\text{rad}}{180^{o}}
    ... and to convert from radians to degrees, multiply by
    \frac{180^{o}}{\pi \,\text{rad}}.

    oh is that why you would multiple 5m/1rad with 220rad/sec? since we have the radian...
    That was just a variation of the original problem of converting from angular speed (rad/sec) to linear speed (m/sec), using a different wheel. (BTW I was actually using the formula that skeeter mentioned: v = r\omega.)

    sorry. i have NEVER taken a trigonometry class before (they didnt teach it in high school for some reason) and i am doing first year calc and getting my butt kicked from the trigonometry portion of it.
    I'm surprised that you were allowed to take calculus at all! In most course descriptions I've seen trig was a prerequisite. Unless this class is a combination of Calc I and Precalc? (There are classes like this that exist - a year-long class integrating precalculus topics with calculus I.)
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Jul 2010
    Posts
    6
    appriciate the answer!

    yeah, my courses/school is weird. i took all of the pre-req math courses but they never taught any trig whatsoever. the last pre-calc class i took was more theory base (intermediate value therom and basic graphs/hows to graph/ "advanced" algebra) but no where did i learn trig.

    The next class i took was a split of Calculus 1 where i only studied the derivatives of polynomials/radicals/power functions and ect with the exclusion of trigonometry and logarithms. I did very well in that class but the second half where it is trig, is really kicking me in the butt. My midterm is compose of half trigonometry related problems (identities, problem solving such as the above and inverse/graphing) while the other half is calculus with trig, related rates/derivatives/linearizion.

    regardless, thank you for the help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Word Problems
    Posted in the Algebra Forum
    Replies: 9
    Last Post: June 28th 2010, 11:12 PM
  2. Problems with integration word problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2010, 05:39 PM
  3. Help with word problems please
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 18th 2009, 02:47 PM
  4. Word problems
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 30th 2007, 09:30 AM
  5. Need Help With 2 Word Problems
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: April 25th 2006, 08:59 PM

Search Tags


/mathhelpforum @mathhelpforum