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    the diagram shows the plan of a school running track. it contains of two straight sections, which are the opposite sides of a rectangle, and two semicircular sections, each of radius r m. the length of the track is 300m and it can be assumed to be very narrow.

    a) show the internal area A m^2, is given by the formula A=300r - πr^2
    b)find in terms of π the maximum value of the internal area?
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    (Original post by hancyk)
    the diagram shows the plan of a school running track. it contains of two straight sections, which are the opposite sides of a rectangle, and two semicircular sections, each of radius r m. the length of the track is 300m and it can be assumed to be very narrow.

    a) show the internal area A m^2, is given by the formula A=300r - πr^2
    b)find in terms of π the maximum value of the internal area?
    What have you tried so far?

    Also, for future questions, it's better to post in the Maths forum here -
    https://www.thestudentroom.co.uk/forumdisplay.php?f=38 (or other relevant subject forum depending on question).
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    (Original post by Goz Unlimited)
    What have you tried so far?

    Also, for future questions, it's better to post in the Maths forum here -
    https://www.thestudentroom.co.uk/forumdisplay.php?f=38 (or other relevant subject forum depending on question).
    i havnt done much as i dont knw where to start from. so a=pi r^2 so for semi circle its 1/2 pi r^2 but there is two semi circles so its would still be pi r^2. i thought u would do 300x2r(the rectangular track)+pi r^2(the two semi circles)
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    (Original post by hancyk)
    i havnt done much as i dont knw where to start from. so a=pi r^2 so for semi circle its 1/2 pi r^2 but there is two semi circles so its would still be pi r^2. i thought u would do 300x2r(the rectangular track)+pi r^2(the two semi circles)
    I agree, we've got two semi circles for part of the area summing to one whole circle of area pi*r^2. 300 is the length of the track made up from two straight sections and two semi circular sections (300 isn't the side of the rectangle - it's the total track perimeter). Can you form an equation for the semi circular sections? If you called one of the straight sections L could you then form a general equation for the perimeter?

    If you haven't already draw a diagram. They always help.
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    (Original post by Goz Unlimited)
    I agree, we've got two semi circles for part of the area summing to one whole circle of area pi*r^2. 300 is the length of the track made up from two straight sections and two semi circular sections (300 isn't the side of the rectangle - it's the total track perimeter). Can you form an equation for the semi circular sections? If you called one of the straight sections L could you then form a general equation for the perimeter?

    If you haven't already draw a diagram. They always help.
    thank you and i've worked out the answer to be as A=300r-pi*r^2
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    (Original post by hancyk)
    thank you and i've worked out the answer to be as A=300r-pi*r^2
    No worries
 
 
 
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