Question

An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45cm, find the area between the two consecutive ribs of the umbrella​

Answer 1

Answer:

There are 8 ribs in umbrella The area between two consecutive ribs is subtending

8

360

0

=45

∘

at the center of assumed flat circle

Area between two consecutive ribs of circle

=

360

45

×πr

2

=

8

1

×

7

22

×(45)

2

=

28

11

×2025

=

28

22275

cm

2

Answer 2

The eight ribs divide the circular umbrella into 8 equal sectors each with r = 45cm and $\sf{\theta = 45°}$

Hence, the area between two consecutive ribs

= area of a sector with r = 45cm and $\sf{\theta = 45°}$

$\longrightarrow$ $\sf{\frac{45}{360} \times \frac{22}{7} \times 45 \times 45 {cm}^{2}}$

$\longrightarrow$ $\sf{\frac{22275}{28} {cm}^{2} }$

$\longrightarrow$ $\sf{795.53 {cm}^{2}}$