P and Q are points on the circumference of a circle, centre O, radius R cm. The minor arc PQ = 20 cm and PÔQ = 48°. Show that R = 23.9, correct to one decimal place. [Figure showing a circle sector POQ with angle 48 degrees, arc length 20, radius R]

1. (a)(i)P and Q are points on the circumference of a circle, centre O, radius R cm. The minor arc PQ = 20 cm and PÔQ = 48°. Show that R = 23.9, correct to one decimal place. [Figure showing a circle sector POQ with angle 48 degrees, arc length 20, radius R][3]
2. (a)(ii)Calculate the area of the minor sector POQ.[2]
3. (a)(iii)The minor sector POQ is removed from the circle and the remaining major sector is shaped to form an open cone of radius r cm. Calculate r. [Figure showing the sector removed, then a cone with radius r][2]
4. (b)(i)[The curved surface area of a cone is πrl, where l is the slant height] Cone A has radius 7.5 cm and height 4 cm. Calculate the curved surface area of cone A. [Figure showing cone A with height 4, radius 7.5][3]
5. (b)(ii)Cone B is geometrically similar to cone A. The ratio curved surface area of cone A : curved surface area of cone B is 64 : 25. Find the height of cone B.[2]

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