Question

What is the area of the remaining portion of a circle of radius 14cm when a square with maximum possible area inscribed in it is removed from it ?(Use ∏=22/7)

• A. 518 cm²
• B. 520 cm²
• C. 224 cm²
• D. 616 cm²

Answer 1

Answer:

C. 224 cm²

We are given a circle of radius 14 cm and a maximum-area inscribed square is removed.

Area of circle

$\text{Area} = \pi r^2 = \frac{22}{7} \times 14^2$
$= \frac{22}{7} \times 196 = 22 \times 28 = 616 \text{ cm}^2$

Square inscribed in circle

For a square inscribed in a circle, diagonal = diameter

Diameter = (2r = 28) cm

So diagonal of square = 28 cm

$\text{Side} = \frac{28}{\sqrt{2}} = 14\sqrt{2}$

Area of square

$\text{Area} = (14\sqrt{2})^2 = 196 \times 2 = 392 \text{ cm}^2$

Remaining area

$616 - 392 = 224$

Final Answer:

224 cm²