Question

The

Answer 1

Answer:

11.34 units²

Step-by-step explanation:

Area of a sector is expressed as $\frac{\theta}{360^{0} }*\pi r^{2}$

Before we can get the area of the circle, we need to find its radius. The radius of the circle can be derived from the equation of the circle given.

$(x+3.5)^{2} + (y-2.82)^{2} =25$

The general form of equation of a circle is given as $(x-a)^{2} + (y-b)^{2} =r^{2}$ where r is the radius of the circle. Comparing the general equation to the given equation to get the radius r;

$r^{2} = 25\\ r = \sqrt{25}\\ r =5$

The radius of the circle is 5

Given the angle subtended by the sector of the circle to be 52°,

Area of the sector = $\frac{52}{360^{0} }*\pi *5^{2}$

$= \frac{52}{360^{0} }*25\pi\\= 0.144 *25 \pi$

$= 0.144 * 25(3.14)\\= 0.144*78.5\\= 11.34units^{2}$

This gives the required area of the sector to nearest hundredth