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# mathematics watch

1. 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?
2. (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).
3. (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)
4. (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.
5. (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
6. (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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