[Volume of sphere = 4/3 πr³] The diagram shows a sphere inside a cube. The sphere touches all 6 faces of the cube. The volume of the cube is 343 cm³. Calculate the volume of the sphere. [Figure showing a sphere inside a cube]

1. (a)[Volume of sphere = 4/3 πr³] The diagram shows a sphere inside a cube. The sphere touches all 6 faces of the cube. The volume of the cube is 343 cm³. Calculate the volume of the sphere. [Figure showing a sphere inside a cube][3]
2. (b)Solid A is mathematically similar to solid B. The volume of solid A is 540 cm³ and its height is 15 cm. The volume of solid B is 1280 cm³. Calculate the height of solid B.[2]
3. (c)[Curved surface area of a cone = πrl] The diagram shows a solid formed by joining a cone to a cylinder. The cone and the cylinder each have radius 6.3 cm. The slant height of the cone is 8.7 cm. The ratio height of cone : height of cylinder = 2 : 3. Calculate the total surface area of the solid. [Figure showing a cone on top of a cylinder, with dimensions 6.3 and 8.7][5]

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