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 rectangle in the running track has only the measurements. the measurements for the rectangle: length is 85m and the width is split in two: 36.41m and 46.41m
Don't understand the "the width is split in two: 36.41m and 46.41m" part.
Do you mean the width to the inside of the track is 36.41 m and the width to the outside of the track is 46.41 m ?
I will assume that.
The semicircles at the ends are alike, so combined they would make up whole circles.
Area of the combined outer circle : radius = 46.41/2 m or 23.205 m
Area = π(23.205)^2 m^2
similarly, the area of the inner circle = π(18.205)^2
The difference in these two areas would be the area of the circular parts of the track. I am sure you can find the width of the two straight tracks, and you know the length is 85 m
Add up the two straights and the difference in the circles and you got it.
Let me know what you got.
the diagram looks like this:
h ttp://oalevelsolutions.com/CIE_GCE_AS_Maths_P1_13_Nov_11_Q_8_files/image001.png
when I meant the width is split in two: 36.41m and 46.41m, I actually meant the diameter is split into two radius: 36.41m and 46.41m
To determine the area of the track, we need to calculate the area of each individual component and then add them together. In this case, we have two parallel sections and two semicircular sections.
1. Start by calculating the area of the rectangle section:
The length of the rectangle is 85m and the width is split into two parts: 36.41m and 46.41m.
To calculate the area of a rectangle, you multiply its length by its width.
So, for the rectangle section, the area would be `(36.41m + 46.41m) * 85m`.
2. Next, calculate the area of each semicircular section:
The semicircular sections are essentially half circles. To calculate their areas, you need to know the radius (half the diameter) of each semicircle.
The radius for the smaller semicircular section can be calculated by subtracting the smaller width (36.41m) from the larger width (46.41m) and dividing it by 2.
So, the radius for the smaller semicircular section is `(46.41m - 36.41m) / 2`.
The radius for the larger semicircular section is equal to the larger width (46.41m) divided by 2.
To calculate the area of a semicircle, you use the formula: `(π * r^2) / 2`, where π is approximately 3.14.
So, for each semicircular section, the areas would be:
- Smaller semicircle: `(3.14 * [(46.41m - 36.41m) / 2]^2) / 2`
- Larger semicircle: `(3.14 * [(46.41m) / 2]^2) / 2`
3. Finally, add the areas of all the components together to get the total area of the track:
Total area = Area of rectangle + Area of smaller semicircle + Area of larger semicircle.
By plugging in the values into the respective formulas and performing the calculations, you can determine the area of the track.