Question

12. The top view of a circular table shown an the right has a radius of 120 cm. Find the area of the smaller segment of the table (shaded region) determined by a 60° arc.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The area is approximately 1300.8 cm² or $2400\pi-3600\sqrt{3}$

Step-by-step explanation:

Consider the provided information.

We need to find the area of the shaded region.

The area of the segment is given as:

$r^2(\frac{\theta \times \pi}{360}-\frac{sin\theta}{2})$

It is given that θ = 60°,  r = 120 cm

Substitute the respective values in the above formula.

$(120)^2(\frac{60 \times \pi}{360}-\frac{sin60}{2})$

$14400(\frac{\pi}{6}-\frac{\sqrt{3}}{4})$

$2400\pi-3600\sqrt{3}$

Now substitute π = 3.14

$2400\times 3.14-3600\times 1.732=1300.8$

Hence, the area is approximately 1300.8 cm² or $2400\pi-3600\sqrt{3}$