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Question id: 86. This question is similar to one that appeared in a IGCSE Extended paper in 2007. The use of a calculator is allowed.

Mensuration

[The surface area of a sphere of radius \(r\) is \(4\pi r^2\) and the volume is \(\frac43\pi r^3\)]

A solid metal sphere has a radius of 7.5 cm.

(a) Calculate the volume of the sphere to the nearest cubic centimetre.

(b) Calculate the surface area of the sphere to the nearest square centimetre.

(c) If one cubic centimetre of the metal has a mass of 4.9 grams calculate the mass of the sphere to three significant figures.

(d) Two of these spheres are placed in the water in a cylindrical tank with base diameter 32cm. Before they were lowered in the depth of the water was 19cm. Calculate the new depth of water in the cylinder when the spheres are fully submerged.

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