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Question

# If the radii of two wheels are in the ratio 3:7, then the ratio of their areas is:

A
9:49
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B
49:9
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C
6:14
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D
3:49
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Solution

## The correct option is A 9:49Given, the ratio of the radii of two wheels is 3:7. Let the radius of the first wheel be 3x, then the radius of the second wheel will be 7x. We know that, Area of a circle = π× (radius)2 Step 1: Area of the first wheel =π×(radius of the first wheel)2 =π×(3x)2 =π×32×x2 =π×9×x2 =9πx2 Step 2: Area of the second wheel =π×(radius of the second wheel)2 =π×(7x)2 =π×72×x2 =π×49×x2 =49πx2 Step 3: Ratio of the areas =Area of the first wheel : Area of the second wheel =9πx2:49πx2 Divide both sides by πx2 =9πx2πx2:49πx2πx2 =9:49 Hence, option (a.) is the correct choice.

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