Difference between the diameters of two circles is 6cm. The difference between their radii is ____.

6cm

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9cm

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4cm

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3cm

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Solution

The correct option is D 3cm
Given that

The difference between the diameters of two circles is 6 cm.

Let the diameters of the circles be $d_{1}$ , $d_{2}$ and their radii be $r_{1}$ , $r_{2}$ respectively.

Then, $d_{1} - d_{2} = 6 c m$

Now, $2 r_{1} = d_{1}$ and $2 r_{2} = d_{2}$ .

On substituting the values we get:

$d_{1} - d_{2} = 6 c m$

$\Rightarrow 2 r_{1} - 2 r_{2} = 6$

$\Rightarrow 2 (r_{1} - r_{2}) = 6$

$\Rightarrow (r_{1} - r_{2}) = \frac{6}{2} = 3 c m$

Hence, the difference between their radii is 3 cm.

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