Question

Find the area of maximum circle that can fit in a square of side 16 cm​

Answer 1

The maximum area of a circle that can fit in a square with sides of 16 cm is found by using the formula A = πr², resulting in an area of 200 cm² when rounded to two significant figures.

Step-by-step explanation:

To find the area of the maximum circle that can fit in a square with a side of 16 cm, we need to understand that the diameter of the circle will be equal to the side length of the square. Since the square's side is 16 cm, the diameter of the circle will also be 16 cm. Therefore, the radius (r) of the circle is half the diameter, which is 8 cm.

Now, to find the area (A) of the circle, we use the area formula for a circle: A = πr².

Plugging in the radius:

1. A = π × (8 cm)²
2. A = 3.1415927... × 64 cm²
3. A = 201.0619298 cm²

However, we must limit our answer to two significant figures because the radius was given to us with two significant figures. This means we round our calculated area to:

A = 200 cm² (to two significant figures).

Answer 2

The area of the largest circle that can fit into a square of side length 16 cm is π(8 cm)² = 64π cm².