Question

Areas of some circles are given below find their diameters.
(1) 176 sq cm
(2) 394.24 sq cm (3) 12474 sq cm
​

Answer 1

Answer:

area of circle=π

4

diameter

2

(1) area of circle = π(diameter)²/4

176 = 22/7 (diameter)²/4

176 × 7 × 4/22 = diameter ²

8 × 7 × 4 = diameter²

diameter = \sqrt{8\times7\times4}

8×7×4

diameter = 4√14 cm

(2) area of circle = 394.24 cm²

so, area of circle = π(diameter)²/4

394.24 = 22/7 × (diameter)²/4

394.24 × 7 × 4/22 = (diameter)²

501.76 = (diameter)²

taking square root both sides ,

diameter = 22.4 cm

(3) area of circle = 12474 cm²

so, area of circle = π(diameter)²/4

12474 = 22/7 × (diameter)²/4

12474 × 7 × 4/22 = diameter²

15876 = diameter ²

taking square root both sides,

diameter = 126 cm

Answer 2

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1] 176 sqcm :

$\large\underline {solution}$

The formula for the Area of cirlcle is π$r^{2}$

Area = π$r^{2}$

176 sqcm = $\frac{22}{7}$ × $r^{2}$

$r^{2}$ = $\frac{176 × 7}{22}$

$r^{2}$ = 56

r = $\sqrt {56}$

$\large\underline {To Find:}$

Diameter of circle = radius × 2

= $\sqrt {56}$ ×2

= $\sqrt {112}$

The diameter of circle is $\sqrt {112}$