Mathematics

Problem

A circular sector has radius

7\,

cm and a central angle of

150^{\circ}

. a. (i) Convert the central angle to radians, expressing the answer as an exact multiple of

\pi

. b. (ii) Find the length of the arc of the sector. c. (iii) Calculate the area of the sector. d. (iv) Keeping the area found in part (iii) unchanged, the central angle is altered to

2.5

radians. Determine the new radius of the sector, correct to one decimal place.

Intuitive explanation

A sector is just a "pie slice" of a circle, and its size depends on two things: how big the circle is (the radius) and how wide the slice is (the central angle). To find the area, you need to figure out what fraction of the whole circle your sector represents, then apply that fraction to the full circle's area formula $\pi r^2$ .

Intuitive explanation

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