mathematics

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?

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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)

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

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?