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ISEE Lower Level
Mathematics Achievement

Calculating Elliptical Track Circumference

Very Hard Measurement Units Of Measurement

A school is organizing a sports day event, and they are required to measure the length of the running track accurately. The track is oval-shaped, with the longer side measuring 200 meters and the shorter side measuring 160 meters. To improve accuracy, the school needs to calculate the average circumference of the track. If they assume that the shape of the track can be approximated to an ellipse, how can they estimate the circumference using the formula for the circumference of an ellipse:

$$ C ext{ (approx)} = ext{π} imes igg(1.5a + 1.5bigg) $$

where $a$ is the semi-major axis and $b$ is the semi-minor axis. Calculate $C$ based on the dimensions provided.

Hint

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