Answer:
Step-by-step explanation:
To find the area of each sector given the radius and central angle, follow these steps:
For question 23:
Given: r = 7 km, θ = 60°
1. Convert the central angle from degrees to radians: 60° = 60° * (π/180) = π/3 radians
2. Calculate the area of the sector using the formula: Area = (θ/360) * π * r^2
Area = (π/3/360) * π * 7^2 = (π/3/360) * π * 49 = π/540 * 49π = 49π^2 / 540
For question 22:
Given: r = 12 yd, θ = 5π/3 radians
1. Calculate the area of the sector using the formula: Area = (θ/2π) * π * r^2
Area = (5π/3/2π) * π * 12^2 = 5/6 * 144π = 120π
For question 24:
Given: r = 7 mi, θ = 225°
1. Convert the central angle from degrees to radians: 225° = 225° * (π/180) = 5π/4 radians
2. Calculate the area of the sector using the formula: Area = (θ/360) * π * r^2
Area = (5π/4/360) * π * 7^2 = (5π/4/360) * 49π = 49π^2 / 288
These calculations provide the area of each sector without rounding.
