Question

a sector with the central angle measure of 4pi/5 (in radians) has a radius of 5 cm. What is the area of the sector? PLS HELP :(

Answer 1

Answer:

Area of the sector = 31.42 cm²

Step-by-step explanation:

Formula for the area of a sector is,

Area = $\frac{\theta}{2\pi }(\pi r^{2} )$

Here θ = central angle subtended by the arc (in radians)

r = radius of the circle

Now substitute the values given in the formula,

Area of the sector = $\frac{\frac{4\pi }{5}}{2\pi }\times \pi (5)^2$

                              = $\frac{4\pi }{10\pi } \times (25\pi)$

                              = $\frac{100}{10}\times \pi$

                              = 10π

                              = 31.416

                              ≈ 31.42 cm²