It is proposed to build a new circular park equal in area to the sum of areas of two circularparks of diameters 16 m and 12 m in a locality. The radius of the new park is
Question
It is proposed to build a new circular park equal in area to the sum of areas of two circularparks of diameters 16 m and 12 m in a locality. The radius of the new park is
Solution
First, we need to find the areas of the two existing parks. The formula for the area of a circle is πr², where r is the radius. The radius is half of the diameter, so the radii of the two parks are 8m and 6m respectively.
The area of the first park is π(8m)² = 64π m². The area of the second park is π(6m)² = 36π m².
The total area of the two parks is 64π m² + 36π m² = 100π m².
Now, we want to find the radius of a new park that has this total area. We can use the formula for the area of a circle again, but this time we'll solve for r:
100π m² = πr² 100 m² = r² r = √100 m² = 10 m.
So, the radius of the new park should be 10 meters.
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