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# [Smart Math] Geometry Problem 9

Here’s and example of a SMART MATH problem for GEOMETRY.

### Problem

A circular lawn of 98 meters is surrounded by a path of 14 meters wide. What is the area of the path in meters2?

1. 9420
2. 9184
3. 9240
4. 9835
5. 9583

### The Usual Method:

The two edges of the path makes concentric circles, one with a radius of 98 meters and another with a radius of 98 + 14 = 112 meters.

Hence area of path = $\pi \times 112^{2}-\pi \times 98^{2}=\pi (112^{2}-98^{2})$

$=\frac{22}{7}(112-98)(112+98)$

$=\frac{22}{7}\times 14\times 210$

= 44 x 210 = 9240 meters2

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Observe that both 98 and 14 are multiples of 7 and when multiplied by $\pi$, will have in the numerator a number which is a multiple of 11 ( $\because$ 22 is in the numerator of the value of $\pi$). Only option ‘3’ is a multiple of 11 and hence it is the answer.