Question

if the area is 48 cm and the radius is of the circle is 4 cm then what is the central angle

Answer 1

Answer:

Step-by-step explanation:

Area of sector = (∅/360°) x πr²

Area of sector = 48cm²

radius = 4cm

π = 3.14

48 =  (∅/360°) x 3.14 x 4 x4

48 = (∅/360°)  x 50.24

48/50.24 =(∅/360°)

0.9554  = (∅/360°)

∅ = 0.9554 x 360 = 343.949≈343.95° ( these is when the angle is in degrees)

if it is radians

area of sector = 1/2r²∅

area of sector = 48

r = radius = 4

area of sector = 1/2r²∅

48 = 1/2 x 4 x4 x∅

48 = 2x4 x∅

48 = 8∅

∅ = 48/8 = 6 radians

the central angle in radians is 6

Answer 2

Answer: The central angle is 343.9 degrees

Step-by-step explanation:

The formula for determining the area of a sector is expressed as

Area of sector = θ/360 × πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius of circle, r = 4 cm

θ = ?

Area of sector = 48 cm²

Therefore,

48 = θ/360 × 3.14 × 4²

48 = θ/360 × 3.14 × 16

48 = 50.24θ/360

θ = (48 × 360)/50.24

θ = 343.9 degrees