A fan-shaped garden forms a sector of a circle of radius 8 m and angle .
(a) Express the angle in radians.
(b) Find the area of the sector.
Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 3.7—radians with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.7—radians and mirrors Paper 1, 2, 3 style where relevant.
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A fan-shaped garden forms a sector of a circle of radius 8 m and angle .
(a) Express the angle in radians.
(b) Find the area of the sector.
(e) Find the time when the rate of coating is at its maximum.
(b) Find the area of the sector.
(b) the area of one shaded segment.
(d) the total area of the shaded regions.
A sector-shaped park has radius m, where , and subtends an angle of radians at its centre in its design. Let m denote the area of this sector and m denote its total perimeter.
A sector of a circle has a radius of 10 cm and subtends an angle of radians at the centre of the circle.
(a) the arc length of the sector.
Solve the equation for , where is in radians.
A circular mirror of radius is centred at . The vertices , and of an equilateral triangular frame lie on the mirror, so the three regions between the frame and the mirror are shaded. Let represent the mass of silver coating, in grams, applied to the mirror after minutes. The application rate is given by .
(a) the magnitude of angle .
(c) the length of minor arc .
(a) the value of if the numerical values and are equal.
(c) a diagram of the circle, shading the given sector that subtends an angle of .