Question

the ratio of the area of a sector of a circle to the area of the circle is 1:4 if the area of the circle is 154 cm square.. the perimeter of the sector is​

Answer 1

Step-by-step explanation:

which is the required ans.

Answer 2

Answer:

perimeter of sector is 25m

Step-by-step explanation:

Given

ratio of the area of a sector of a circle to the area of the circle=1:4

=1/4

Area of a sector circle =

$\frac{\pi {r}^{2} \: theta }{360}$

Area of the circle=

$\pi {r}^{2} = 154$

${r}^{2} = \frac{154}{\pi}$

${r}^{2} = 49 \\ r = 7$

ratio of the area of a sector of a circle to the area of the circle=1:4

$\frac{ \frac{\pi {r}^{2}theta }{360} }{\pi {r}^{2} } = \frac{1}{4}$

$theta = \frac{360}{4} = 90$

length of the arc=

$= \frac{\pi \: r \: theta}{180}$

$= \frac{\pi \times 7 \times 90}{180 } = 11$

Perimeter of the sector=

$7 + 7 + 11 = 25$

Therefore perimeter of sector is 25m

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