Question

An umbrella has \[8\] ribs that are equally shaped. Assuming the umbrella to be a flat circle of radius of \[45{\text{ }}cm\], find the area between two consecutive ribs of the umbrella.

Answer 1

Hint: We have to calculate the area of the full circle and then to find the area between \[2\] ribs we will have to divide the area of the circle by \[8\]. As it is said that the umbrella has \[8\] ribs of equal shapes. So the total area of \[8\] ribs will be the same as the area of the umbrella. By putting the values of different parameters we can get the value of the area of rib.


Complete step by step solution:
Radius of the circle is \[45{\text{ }}cm\].
A circle is drawn accordingly.
And it is divided into \[8\] equal parts or ribs. Each of those is showing in the figure.
        

Area of the circle
As there are \[8\] ribs in the circle, the area is divided into \[8\] parts,
Area of rib $ = \dfrac{1}{8} \times {\text{Area of umbrella}}$
$ = \dfrac{1}{8} \times \pi {r^2}$
$ = \dfrac{1}{8} \times \pi {r^2}$
$ = \dfrac{1}{8} \times \dfrac{{22}}{7} \times {\left( {45} \right)^2}{\text{ }}\left[ {{\text{radius = 45 cm}}} \right]$
$ = \dfrac{1}{8} \times \dfrac{{22}}{7} \times 2025$
$ = \dfrac{{{{22275}}}}{{{{28}}}}{\text{ c}}{{\text{m}}^2}$
 \[ = {\text{ }}795.5{\text{ }}c{m^2}\]
So the area of rib is \[795.5{\text{ }}c{m^2}\]

Note: Umbrella is circular so area can be calculated and as the umbrella is having \[8\] equal parts, so dividing area of the circle by \[8\] we will get the area of rib. We have to keep in mind that we will get the area of the circle by multiplying the area of the rib with \[8\]. One thing to remember is the total area of the circle is the same as the total area of \[8\] ribs.