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Two circles are drawn inside a big circle with diameters $23$ rd and $13$ rd of the diameter of the big circle as shown in figure. Find the area of the shaded portion, if the length of the diameter of the big circle is $18 cm$ .

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36 π c m 2

40 π c m 2

46 π c m 2

49 π c m 2

answer is A.

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Detailed Solution

Given two circles are drawn inside a big circle with diameters

23

rd and

13

rd of the diameter of the big circle.
Two circles are drawn inside a big circle with diameters 2/3rd and 1/3rd of the diameter of the big circle as shown in Fig.18. Find the area of the shaded portion, if

Two circles are drawn inside a big circle with diameters 2/3rd and 1/3rd of the diameter of the big circle as shown in Fig.18. Find the area of the shaded portion, if

Assume, shaded area = A.
The diameter of big circle is 18 cm.
Then, diameter of circle having

rd diameter as of big circle

= d_{1}

\Rightarrow d_{1} = \frac{2}{3} \times 18 cm

Therefore, radius is,

r 1 = 12 × 23 × 18

cm.
The diameter of circle having

13

rd diameter as of big circle =

d_{2}

\Rightarrow d_{2} = \frac{1}{3} \times 18 cm

Therefore, radius is,

r 2 = 12 × 13 × 18

cm.
Area of circle is

π r 2

.
Area of shaded region = area of big circle – area of circle having

23

rd diameter as of big circle – area of circle having

13

rd diameter as of the big circle.

⇒ A = π 1822 − π × 12 × 23 × 18 2 + π × 12 × 13 × 18 2

⇒ A = π 92 − π × 62 + π × 32

⇒ A = 81 π − 36 π + 9 π

⇒ A = 81 π − 45 π

⇒ A = 36 π

Therefore, the area of shaded portion is

36 π c m 2

.
Hence, option 1 is correct.

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