Question

area of rectangle and the area of a circle are equal if the dimensions of the rectangle are 14 cm * 11 cm then the radius of the circle is

Answer 1

$<b><font color = "red" >Hi friends!$

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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


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

Hence, radius of circle = 7 cm

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Answer 2

Radius of circle is 7 cm.

Given:

• A rectangle having length 14 cm and breadth 11 cm.
• A circle
• Both have equal area.

To find:

• Radius of circle.

Solution:

Formula to be used:

1. Area of rectangle = Length×breadth
2. Area of circle= π r²

Step 1:

Find area of rectangle.

length (l)= 14 cm

breadth (b)= 11 cm

Area of rectangle = 14×11 cm²

Step 2:

Find Area of circle.

Let radius of circle is r.

Area of circle = π r²

Step 3:

Equate result of step 1 and step 2.

$\pi \: {r}^{2} = 14 \times 11$

or

$\frac{22}{7} {r}^{2} = 14 \times 11$

or

${r}^{2} = \frac{14 \times 11 \times 7}{22}$

or

${r}^{2} = 49$

or

$r = \pm \: 7 \: cm$

Discard the -ve value.

Thus,

Radius of circle is 7 cm.

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