Question

9. A circle is inscribed in a square of side 56 cm. Find the maximum area of circle. (a) 2242cm (b) 3080 cm (c) 2876 cm (d) 2464 cm​

Answer 1

Answer:

Given :-

• A circle is inscribed in a square of side 56 cm.

To Find :-

• What is the maximum area of circle.

Solution :-

First, we have to find the radius of a circle :

Given :

• Diameter = 56 cm

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{Radius =\: \dfrac{Diameter}{2}}}$

$\implies \sf Radius =\: \dfrac{56}{2}$

$\implies \sf Radius =\: \dfrac{28}{1}$

$\implies \sf\bold{Radius =\: 28\: cm}$

Hence, the radius of circle is 28 cm .

Now, we have to find the maximum area of circle :

Given :

• Radius = 28 cm

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{Area_{(Circle)} =\: {\pi}r^2}}$

where,

• π = Pie or 22/7
• r = Radius

So, by putting those values we get,

$\implies \sf Area_{(Circle)} =\: \dfrac{22}{7} \times (28)^2$

$\implies \sf Area_{(Circle)} =\: \dfrac{22}{7} \times (28 \times 28)$

$\implies \sf Area_{(Circle)} =\: \dfrac{22}{7} \times 784$

$\implies \sf Area_{(Circle)} =\: \dfrac{17248}{7}$

$\implies \bold{Area_{(Circle)} =\: 2464\: cm^2}$

$\sf\bold{\underline{\therefore\: The\: area\: of\: circle\: is\: 2464\: cm^2}}$

Hence, the correct options is option no (d) 2464 cm² .