4 (a) O O NOT TO SCALE x° 7.5 cm 7.5 cm A B B 1.5 cm A The diagram shows a sector of a circle that is made into a cone by joining OA to OB. The sector angle is x° and the radius of the sector is 7.5 cm. The base radius of the cone is 1.5 cm. Calculate the value of x. x = ................................................ [3] (b) NOT TO SCALE The diagram shows a cylinder with radius 8 cm inside a sphere with radius 17 cm. Both ends of the cylinder touch the curved surface of the sphere. (i) Show that the height of the cylinder is 30 cm. [2] © UCLES 2023 0580/42/O/N/23 7 (ii) Calculate the volume of the cylinder as a percentage of the volume of the sphere. 4 [The volume, V, of a sphere with radius r is V = rr3.] 3 ............................................. % [4] (c) 15 cm NOT TO SCALE The diagram shows a solid sphere with radius 6 cm inside a cube with side length 20 cm. The cube contains water to a depth of 15 cm. The sphere is removed. Calculate the new depth of water in the cube. 4 [The volume, V, of a sphere with radius r is V = rr3.] 3 ............................................ cm [3] © UCLES 2023 0580/42/O/N/23 [Turn over 8