Find the area of the shaded part (the two diagrams are circular sectors) given that central angle is 60 degrees and the bigger radius 7cm, width of the shaded portion is 2cm.
what do you mean width...the difference in radai?
if so, then take the area of the larger circle sector (area sector=PI*r^2*angle/360 )
minus the area of the sector of the smaller radius.
overall, you ought to have this
area shaded=PI*60/360 (9^2-7^2) IF I understand the figure.
To find the area of the shaded part, we need to calculate the area of the larger sector and subtract the area of the smaller sector.
Step 1: Calculate the area of the larger sector.
The formula to calculate the area of a sector is A = (θ/360) * π * r^2, where θ is the central angle and r is the radius.
Given:
θ = 60 degrees
r = 7 cm
Convert the angle from degrees to radians: θ_rad = θ * π/180 = 60 * π/180 = π/3
Calculate the area of the larger sector: A_large = (π/3/360) * π * 7^2
Step 2: Calculate the area of the smaller sector.
Since the width of the shaded portion is 2 cm, the radius of the smaller sector will be 7 cm - 2 cm = 5 cm.
Using the same formula as before, but with the new values, we can calculate the area of the smaller sector: A_small = (π/3/360) * π * 5^2
Step 3: Calculate the area of the shaded part.
Finally, subtract the area of the smaller sector from the area of the larger sector to find the area of the shaded part: A_shaded = A_large - A_small.
Let's calculate the values:
A_large = (π/3/360) * π * 7^2 = (π/180) * π * 7^2
A_small = (π/3/360) * π * 5^2 = (π/180) * π * 5^2
A_shaded = A_large - A_small
Please calculate the values to find the area of the shaded part.