Question

Trig: A sector of a circle has area 25 cm2 and centralangle

0.5 radians. Find its radius and arc length.

Answer 1

To find the radius and arc length of a sector of a circle, we use formulas related to the circumference and central angle of a circle. The radius of the sector is 10 cm and the arc length is 5 cm.

Step-by-step explanation:

To find the radius and arc length of a sector of a circle, we need to use the formulas related to the circumference and central angle of a circle. The formula for the area of a sector is given by:

Area = (θ/2) * r^2

where θ is the central angle and r is the radius of the circle. We are given that the area of the sector is 25 cm^2 and the central angle is 0.5 radians. Setting up this equation, we get:

25 = (0.5/2) * r^2

Simplifying, we find:

r^2 = 100

Taking the square root of both sides, we find:

r = 10 cm

To find the arc length, we use the formula:

Arc Length = θ * r

Substituting the values, we find:

Arc Length = 0.5 * 10 = 5 cm

Answer 2

Answer: Radius = 10 cm and Arc length = 5 cm

Step-by-step explanation:

The area of a sector with radius r and central angle
`\theta` (In radian) is given by :-

`A=(1)/(2)r^2\theta`

Given : A sector of a circle has area
`25 cm^2` and central angle 0.5 radians.

Let r be the radius , then we have

`25=(1)/(2)r^2(0.5)\\\\\Rightarrow\ r^2=(2*25)/(0.5)\\\\\Rightarrow\ r^2=(50)/(0.5)=100\\\\\Rightarrow\ r=√(100)=10\ cm`

Thus, radius = 10 cm

The length of arc is given by :-

`l=r\theta=10*0.5=5\ cm`

Hence, the length of the arc = 5 cm