This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here is the solution to the problem: Given: Area of sector = 427 cm^2 Radius of circular metal sheet (R) = 17 cm (This becomes the slant height l of the cone) = 3.142 All answers to be rounded to three significant figures. a) The angle of the sector Let be the angle of the sector in degrees. The formula for the area of a sector is: Area = ()/(360^) R^2 Substitute the given values: 427 = ()/(360) × 3.142 × (17)^2 427 = ()/(360) × 3.142 × 289 427 = ( × 907.998)/(360) Now, solve for : = (427 × 360)/(907.998) = (153720)/(907.998) ≈ 169.299^ Rounding to three significant figures: ≈ 169^ The angle of the sector is $169^