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Picture this: a brand-new circular park that’s as spacious as two others put together—one’s 16m wide and the other’s 12m.
It is proposed to build a new circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park is
The radius of the new park is 10 metres.
To find the radius of the new circular park, we first calculate the areas of the two circular parks with diameters of 16 meters and 12 meters.
For the first park with a diameter of 16 meters:
Radius_1 = 16/2 = 8 meters
Area_1 = 64π square meters
For the second park with a diameter of 12 meters:
Radius_2 = 12/2 = 6 meters
Area_2 = 36π square meters
Now, we add the areas of the two parks to find the total area of the new park:
Total_area = Area_1 + Area_2
= 64π + 36π
= 100π square meters
To find the radius (r_new) of the new park, we use the area formula rearranged to solve for the radius:
Total_area = π × r_new^2
100π = π × r_new^2
r_new^2 = 100
r_new = √100 = 10 meters
So, the radius of the new circular park is 10 meters.
How to Calculate the Area of Circles?
There are two main ways to calculate the area of a circle:
1. Using the radius:
The most common way to calculate the area of a circle is by using the formula:
Area = πr²
where:
- π (pi) is a mathematical constant approximately equal to 3.14159.
- r is the radius of the circle, which is the distance from the center of the circle to any point on the edge.
2. Using the diameter:
If you only know the diameter of the circle (the distance across the circle passing through the center), you can first calculate the radius by dividing the diameter by 2:
radius = diameter / 2
Then, you can use the formula above to calculate the area using the radius.
Here are some additional things to keep in mind:
- Make sure you use consistent units for both the radius and the area. For example, if your radius is in centimeters, your area will be in square centimeters.
- You can use a calculator to approximate the value of pi to several decimal places. However, most calculators have a pi button that you can use for more accurate calculations.
- There are also online calculators that can calculate the area of a circle for you if you enter the radius or diameter.
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Source: Math Hello Kitty
Categories: Math
