Question

in figure 'o' is the centre of circle the area of sector OAPB is 10/72 of the area of circle find x .
​

Answer 1

Step-by-step explanation:

Area of the sector=

18

5

×area of circle

⇒

360

θ

×πr

2

=

18

5

×πr

2

⇒θ=

18

5

×360=100

∘

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Answer 2

Given:

Area of the sector$\[ = \frac{{10}}{{72}}\]$

To find: the area of the circle.

Solution:

Assume that the area of the sector is x.

Draw the required figure.

Know that from the question,

Area of the sector $\[ = \frac{{10}}{{72}}\]$ of the area of the circle

$\[ \Rightarrow \pi {r^2} \times \frac{x}{{360}} = \frac{{10}}{{72}} \times \pi {r^2}\]$

$\[ \Rightarrow \frac{x}{{360}} = \frac{{10}}{{72}}\]$

$\[ \Rightarrow x = \frac{{10 \times 360}}{{72}}\]$

$\[ \Rightarrow x = {50^ \circ }\]$

Hence, the value of x is ${50^ \circ }$.