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The given figure is made up of a rectangle and $2$ identical circles. If the length of the rectangle is $28 cm$ , what is the area of the region in the rectangle excluding the areas occupied by the circle?

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84 c m^{2}

105 c m^{2}

152 c m^{2}

123 c m^{2}

answer is A.

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Detailed Solution

Given,

Radius of the circle

= \frac{length of rectangle}{4}

.
Thus radius of the circle and breath of the rectangle are

7

and

14

respectively.
Required Area

=

Area of rectangle

- 2

\times

area of circle.
Area of a rectangle is (length)×(breadth).
Area of a circle is

π r^{2}

\Rightarrow

Required Area

= 28

\times

14 - 2

\times

π r^{2}

\Rightarrow

Required Area

= 392 - 2 \times \frac{22}{7} \times 7 \times 7

\Rightarrow

Required Area

= 392 - 308

\Rightarrow

Required Area

= 84

{cm}^{2}

Hence, option 1 is correct.

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The given figure is made up of a rectangle and 2 identical circles. If the length of the rectangle is 28 cm, what is the area of the region in the rectangle excluding the areas occupied by the circle?

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The given figure is made up of a rectangle and $2$ identical circles. If the length of the rectangle is $28 cm$ , what is the area of the region in the rectangle excluding the areas occupied by the circle?