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Question
A park is in the form of rectangle 120m × 100m. At the centre of park there is a circular lawn. The area of park excluding lawn is 8700m2. Find the radius of circular lawn.
Solution
Dimensions of rectangular park length = 120m
Breadth = 100m
Area of park = l × b
= 120 × 100 = 12000𝑚2.
𝐿𝑒𝑡 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑙𝑎𝑤𝑛 𝑏𝑒 𝑟
Area of circular lawn = 𝜋𝑟2
Area of remaining park excluding lawn = (area of park) – (area of circular lawn)
⇒ 8700 = 12000 – 𝜋r2
⇒ 𝜋r2 = 12000 – 8700 = 3300
⇒`22/7× r^2 = 3300`
⇒ `r^2` = 150 × 7 = 1050
⇒ `r = sqrt(1050) = 5sqrt(42)` 𝑚𝑒𝑡𝑟𝑒𝑠
∴ radius of circular lawn = 5`sqrt(42)` metres.
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