Question 67

The difference between the areas of two concentric circles is $$88 cm^{2}$$. If the radius of the inner circle is 6 cm, then the area (in $$cm^{2}$$) of the larger circle is closest to: (Taken $$\pi=\frac{22}{7}$$)

Let the radius of the larger circle be (R) cm.

Since the circles are concentric, the difference between their areas is $$\pi R^2-\pi(6)^2=88.$$

Substituting $$\pi=\dfrac{22}{7}$$
,

$$\frac{22}{7}(R^2-36)=88.$$

or, $$ R^2-36=88\times\frac{7}{22}=28.$$

or, $$ R^2=64.$$

Hence, the area of the larger circle is $$ \pi R^2=\frac{22}{7}\times64=\frac{1408}{7}\approx201.14\text{ cm}^2.$$

Therefore, the area of the larger circle is closest to $$\boxed{201\text{ cm}^2}.$$

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