Question

An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 42 $cm$, find the area in $c{m}^2$ between the two consecutive ribs of the umbrella. (Take $\pi =\frac{22}{7}$)

• A. 693 $c{m}^2$
• B. 893 $c{m}^2$
• C. 862 $c{m}^2$
• D. 993 $c{m}^2$

Answer 1

The correct option is A 693 $c{m}^2$

Given: Radius ($r$) = 42 $cm$
There are 8 ribs and the angle subtended between consecutive ribs = $\frac{360}{8}$ = ${45}^{\circ }$ .

Consider, Area between consecutive ribs as Area of sector

$\therefore$ Area between consecutive ribs
= $\frac{{\theta }^{\circ }}{{360}^{\circ }}\times \pi \times (r{)}^2$
=$\frac{45}{360}$ × $\frac{22}{7}$ × ${42}^2$ = 693 $c{m}^2$