Question

The area of the greatest circle which can be inscribed in a square whose perimeter is $120cm$ is

• A. $\frac{22}{7}\times {\left(\frac{7}{2}\right)}^{2}c{m}^2$
• B. $\frac{22}{7}\times {\left(\frac{9}{2}\right)}^{2}c{m}^2$
• C. $\frac{22}{7}\times {\left(\frac{15}{2}\right)}^{2}c{m}^2$
• D. $\frac{22}{7}\times {\left(15\right)}^{2}c{m}^2$

Answer 1

The correct option is D $\frac{22}{7}\times {\left(15\right)}^{2}c{m}^2$

Given square whose perimeter is $120cm$.
Then side of square $=\frac{120}{4}=30cm$
The radius of the greatest circle which can be inscribed in a square $=\frac{30}{2}=15cm$
Then area of the greatest circle which can be inscribed in a square $=\pi r^2=\pi (15{)}^2=\frac{22}{7}\times (15{)}^{2}c{m}^2$