Results 1 to 7 of 7

Math Help - Area Problem

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    117

    Area Problem

    I have been stuck on this problem. Any help to get me started would be appreciated thanks.

    A student in a stationary hot-air balloon is momentarily fixed at 1,325-ft elevation above a level piece of land. The pilot looks down( 60 degrees from the horizontal) and turns laterally 360 degrees.

    a) how many acres are contained within the core generated by his line of sight?

    b) how high would the balloon be if, when performing the same procedure an area 4 times greater is encompassed? (hint: 1 acre= 43,559.5 ft sq.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,061
    Thanks
    900
    you made a sketch, right?

    \tan(60) = \frac{1325}{r}

    where r is the radius of land on the surface within the "cone".

    solve for r, then find the area of the circular plot of land in square feet ... you'll have to convert that to acres.

    for an area 4 times greater, r would have to be doubled, right? why?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2008
    Posts
    117
    Quote Originally Posted by skeeter View Post
    you made a sketch, right?

    \tan(60) = \frac{1325}{r}

    where r is the radius of land on the surface within the "cone".

    solve for r, then find the area of the circular plot of land in square feet ... you'll have to convert that to acres.

    for an area 4 times greater, r would have to be doubled, right? why?
    Yes I made a sketch and got r=764.98..so then I would need to use the surface area of a cone formula? I get 3676972.5 when I used the formula for that. So if I am converting correctly I get 84.4 acres. Is this correct?

    r doubled? why wouldnt it have to be multiplied by 4?

    thanks for quick reply too
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,061
    Thanks
    900
    not the surface area for a cone ... you're only trying to find the area of the land which is enclosed by a circle.

    how much larger is \pi(2r)^2 than \pi r^2 ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2008
    Posts
    117
    Quote Originally Posted by skeeter View Post
    not the surface area for a cone ... you're only trying to find the area of the land which is enclosed by a circle.

    how much larger is \pi(2r)^2 than \pi r^2 ?


    ok so i just need to use A= \pi r^2 to find the area that he is looking at?

    and \pi(2r)^2 is twice the radius
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,061
    Thanks
    900
    Quote Originally Posted by ur5pointos2slo View Post
    ok so i just need to use A= \pi r^2 to find the area that he is looking at?
    and \pi(2r)^2 is twice the radius
    yes, just \pi r^2

    twice the radius results in four times the area.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Sep 2008
    Posts
    117
    Quote Originally Posted by skeeter View Post
    yes, just \pi r^2

    twice the radius results in four times the area.
    You are good. Thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area problem
    Posted in the Geometry Forum
    Replies: 7
    Last Post: August 5th 2011, 03:19 PM
  2. Area Problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 23rd 2009, 11:02 PM
  3. Differential eq problem and area problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 5th 2009, 05:46 PM
  4. Replies: 4
    Last Post: December 16th 2008, 11:45 PM
  5. Please help- area problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 29th 2008, 12:49 PM

Search Tags


/mathhelpforum @mathhelpforum