2 small circular parks of diameters 16 m and | vedclass

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(A) The area of a circle is given by the formula $A = \pi r^2$,where $r$ is the radius.For the first park,the diameter is $16 \ m$,so the radius $r_1

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(A) The area of a circle is given by the formula $A = \pi r^2$,where $r$ is the radius.For the first park,the diameter is $16 \ m$,so the radius $r_1 = 16 / 2 = 8 \ m$.The area of the first park is $A_1 = \pi (8)^2 = 64\pi \ m^2$.For the second park,the diameter is $12 \ m$,so the radius $r_2 = 12 / 2 = 6 \ m$.The area of the second park is $A_2 = \pi (6)^2 = 36\pi \ m^2$.The total area of the two parks is $A_{total} = 64\pi + 36\pi = 100\pi \ m^2$.Let the radius of the new park be $R$. Since the new park occupies the same space,its area must be equal to the total area of the two small parks:$\pi R^2 = 100\pi$$R^2 = 100$$R = \sqrt{100} = 10 \ m$.Therefore,the radius of the new park is $10 \ m$.

$2$ small circular parks of diameters $16 \ m$ and $12 \ m$ are to be replaced by a bigger circular park. What would be the radius of this new park,if the new park occupies the same space as the two small parks?

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