there is a diagram.
the running track in the diagram consists of two parallel sections with semicircular sections at each end. determine the area of the track.
the diagram looks like this:
h ttp://oalevelsolutions.com/CIE_GCE_AS_Maths_P1_13_Nov_11_Q_8_files/image001.png
there is no space between h and ttp in the link above
The rectangle in the running track has only the measurements. the measurements for the rectangle: length is 85m and the diameter is split into two radius: 36.41m and 46.41m
If the two radii are not equal, then the interior is not a rectangle. Since the diagram just shows one r, I suspect a typo.
In any case, what is your question?
The length of the track is two lengths of a rectangle that is x by 2r, plus a full circle of radius r, right?
That would be 2x + 2pi r
To determine the area of the track, we need to calculate the areas of each individual shape in the diagram and then sum them up.
Let's break down the diagram into its components:
1. Rectangle: The length of the rectangle is given as 85m. The width of the rectangle is the difference between the two semicircular sections at the ends of the track. Since the radius of the smaller semicircle is given as 36.41m and the larger semicircle is given as 46.41m, their difference is 46.41m - 36.41m = 10m. So the width of the rectangle is 10m. To calculate the area of the rectangle, we multiply its length and width: 85m * 10m = 850m².
2. Semicircular sections: The area of a semicircle is given by the formula (π * r²) / 2, where r is the radius of the semicircle. The smaller semicircular section has a radius of 36.41m, so its area is (π * 36.41m²) / 2. Similarly, the larger semicircular section has a radius of 46.41m, so its area is (π * 46.41m²) / 2.
Now, add up the areas of the rectangle and the two semicircular sections to find the total area of the track:
Total area = Area of rectangle + Area of smaller semicircular section + Area of larger semicircular section
Total area = 850m² + [(π * 36.41m²) / 2] + [(π * 46.41m²) / 2]
Now, substitute the value of π (pi) as 3.14 and calculate the numerical value of the areas.
Note: Please keep in mind that the accuracy of the final answer will depend on the precision of the provided measurements and the value of π used for calculation.