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Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are 14 cm × 11 cm, then radius of the circle is:

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21 cm

10.5 cm

14 cm

7 cm

answer is D.

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Detailed Solution

Given, the area of a rectangle and the area of a circle are equal.
Dimensions of the rectangle = 14 cm × 11 cm.
Now, as per the given dimensions of the rectangle, its area will be,
= Length x Breadth

= 14 × 11 = 154

Next, the area of a circle with ‘r’ radius is given as

π r 2

.
Now, as it is given that the area of the circle is the same as that of the rectangle, so we have,

π r 2 = 154 227 × r 2 = 154 r 2 = 154 × 7 22 r 2 = 7 × 7 r = 7 × 7 r = 7

So, the radius of the circle is found as 7 cm.
Hence, the correct option is (4).

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