Question

2. Area of a rectangle and the area of a cirde are equal
dimensions of the rectangle are 14cm x 11 cm, the
of the circle is
(a) 21 cm (b) 10,5 cm (c) 14 cm (d) 7 cm​

Answer 1

Answer:

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_______________________

Area of rectangle = area of circle.

Now,

Length of rectangle = 14 cm.

Breadth of the rectangle = 11 cm.

Area of rectangle = length × breadth

⇒ 14 × 11

⇒ 154 cm²

Now,

Area of circle = 154 cm²

⇒πr² = 154 cm²

\begin{gathered}⇒ \frac{22}{7} \times r {}^{2} = 154 \\ \\ ⇒22r {}^{2} = 154 \times 7 \\ \\ ⇒22r {}^{2} = 1078 \\ \\ ⇒r {}^{2} = \frac{1078}{22} \\ \\ r {}^{2} = 49 \\ \\ ⇒r = \sqrt{49} \\ \\ \therefore r = 7\end{gathered}

⇒

7

22

×r

2

=154

⇒22r

2

=154×7

⇒22r

2

=1078

⇒r

2

=

22

1078

r

2

=49

⇒r=

49

∴r=7

Hence, radius of circle = 7 cm

_______________________

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Answer 2

Answer:

Area of rectangle = 14×7=98 cm

2

Radius of semicircle =

2

7

cm

Area of semicircle =

2

1

×

7

22

×

2

7

×

2

7

=

4

77

=19.25 cm

2

Radius of quarter circle =7 cm

Area of quarter circle =

4

1

×

7

22

×7×7=38.5 cm

2

Therefore,

Required area = 98−19.25−38.5=40.25 cm

2

Step-by-step explanation:

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