Multiple choice

Suppose a region is formed by removing a sector of 20° from a circular region of radius 30 feet. What is the area of this new region?

  1. 150π square feet

  2. 550π square feet

  3. 650π square feet

  4. 850π square feet
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D Correct answer
Explanation

Area of circle = pi * r^2 = pi * 30^2 = 900pi. Sector removed = (20/360) * 900pi = (1/18) * 900pi = 50pi. Remaining area = 900pi - 50pi = 850pi.

AI explanation

The area of the circular region before removing the sector is calculated using the circle area formula pi * r^2, yielding pi * 30^2 = 900 square feet. The region is formed by removing a 20 degree sector, so the area of this removed sector is (20/360) * 900 = 50 square feet. The area of the new region is the total area minus the removed sector area: 900 - 50 = 850 square feet.

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