Question

There are two circular playgrounds in a city. Radius of one playground is $50\text{m}$ and radius of another playground is $100\text{m}$. Sum of areas of these two playgrounds is

• A. an irrational number
• B. a rational number
• C. neither irrational nor rational number

Answer 1

The correct option is A an irrational number

Area of playground with $50\text{m}$ radius $=\pi r^2=\pi (50{)}^2=2,500\pi$

Area of playground with $100\text{m}$ radius $=\pi r^2=\pi (100{)}^2=10,000\pi$

Sum of areas of these two playgrounds $=2,500\pi +10,000\pi =12,500\pi$

We know that $\pi =\mathrm{3.14159.....}$ is a non-terminating and non-repeating number that we call an irrational number.

Hence, $12,500\pi$ is an irrational number.