Question

If the perimeter of a sector of a circle of
radius 6.4 cm is 30 cm, then the area of
corresponding sector is​

Answer 1

The area of  corresponding sector is​ "$55.04cm^{2}$".

Step-by-step explanation:

Given,

Radius(r) = 6.4 cm and perimeter of a sector of a circle = 30 cm

To find, the area of  corresponding sector = ?

∴ Arc length of sector = Perimeter - 2r

= 30 cm - 2 × 6.4 cm = 17.2 cm

∴ $\theta =\dfrac{Arc length}{Radius}$ =$\dfrac{17.2}{6.4} </strong>=2.6875$

Area of sector = $\pi r^{2}$

=$\pi 6.4^{2}=<strong>4096 \pi cm^{2}$

Area of sector = $\dfrac{\theta}{2\pi } \times area of circle$

=$\dfrac{2.6875}{2\pi } \times40.96 \pi$

= 55.04$cm^{2}$

Hence,  the area of  corresponding sector is​ $55.04cm^{2}$.

Answer 2

Step-by-step explanation:

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