Question

The equation of a circle is given by (x + 3.5) ^ 2 + (y - 2.82) ^ 2 = 25 What is the area of a 52 degrees sector of this circle? Round to the nearest hundredth of a square unit.

Answer 1

Answer:

≈ 11.34 units²

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 3.5)² + (y - 2.82)² = 25 ← is in standard form

with r² = 25 ⇒ r = $\sqrt{25}$ = 5

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × $\frac{52}{360}$

   = π × 5² × $\frac{52}{360}$

   = π × 25 × $\frac{52}{360}$

   = $\frac{25(52)\pi }{360}$

   ≈ 11.34 units² ( to the nearest hundredth )