Question

I will give you brainiest if you can answer the questions below.

An arc AB subtends an angle of 2.4 radians at the center O of a circle with radius 50 cm. Find the area and perimeter of sector AOB.

The bottom of a pendulum traces an arc 3 feet in length when the pendulum swings through an angle of ½ radian. What is the number of feet in the length of the pendulum?

Answer 1

Answer:

a. i. 3000 cm² ii. 220 cm  b.  6 feet

Step-by-step explanation:

A. i. The area of the sector AOB is A = ¹/₂r²θ where r = radius of circle = 50 cm and θ = angle subtended at the center of the circle by the sector in radians = 2.4 radians.

So, A = ¹/₂r²θ

= ¹/₂(50 cm)² × 2.4 rad

= ¹/₂ × 2500 cm² × 2.4 rad

= 1250 cm² × 2.4 rad

= 3000 cm²

ii. The perimeter of the sector is P = 2r + rθ = (2 + θ)r

substituting r and θ, we have

P = (2 + θ)r

= (2 + 2.4) × 50 cm

= 4.4 × 50 cm

= 220 cm

B. Since length of an arc L = rθ where r = radius = length of pendulum and θ = angle swept by pendulum =  ½ radian and length of the arc swept = 3 feet, the radius is

r = L/θ

= 3 feet ÷ ½ rad

= 3 × 2

= 6 feet