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