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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.

(A)${\text{ }}765.53c{m^2}$

(B)${\text{ 895}}.63c{m^2} $

(C)${\text{ }}795.53c{m^2}$

(D)${\text{ 700}}{\text{.03}}c{m^2}$

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Last updated date: 14th Jul 2024
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Hint: First assume the area of 2 consecutive ribs to be ‘x’ and find the area of the umbrella based on ribs. Later find the area of the umbrella which makes a circle by using the formula ‘$\pi {r^2}$’. Compare the 2 areas to find the required solution.

Complete step by step answer:

As we can see from the above figure that an umbrella having 8 ribs will have 8 different sectors.

And as given in the question area all ribs are equally placed.

So let the area between any two consecutive ribs be $x{\text{ }}c{m^2}$.

So, as ribs are equally placed then the area of all sectors will be the same.

Hence the total area of the umbrella will be $8x{\text{ }}c{m^2}$.

$ \Rightarrow$ Area = $8x{\text{ }}c{m^2}$..................................(1)

The radius of the umbrella is given as, r = 45cm. 

As we know here umbrella is a flat circle so, its area will be $\pi {r^2}$

$ \Rightarrow Area = \pi {r^2} = \dfrac{{22}}{7}*{(45)^2}c{m^2} = 6364.28c{m^2} $

Comparing Area with equation (1) we get,

$\Rightarrow 8x = 6364.28 $

$\Rightarrow x = 795.53{\text{ }}c{m^2} $

Hence the area between two consecutive ribs will be $795.53{\text{ }}c{m^2}$. 

Correct answer is option C.

NOTE: - Whenever we come up with this type of problem we should draw a rough figure at starting. It will give us a clear picture of a problem. Assume the area of rib with some value and find out the area of the umbrella to find the solution.