## IGCSE Mathematics 0580/04/SP/20 Q10

**10 (a) **Show that the volume of a metal sphere of radius 15cm is 14140cm3, correct to 4 significant figures.

[The volume, *V*, of a sphere with radius *r *is *V *= 34 π*r*3.]

**(b) (i) **The sphere is placed inside an empty cylindrical tank of radius 25 cm and height 60 cm. The tank is filled with water.

Calculate the volume of water needed to fill the tank.

**(ii) **The sphere is removed from the tank.

Calculate the depth, *d*, of water in the tank.

**(c) **The diagram below shows a solid circular cone and a solid sphere.

** **

The cone has radius 5*x *cm and height 12*x *cm.

The sphere has radius *r *cm.

The cone has the same total surface area as the sphere.

Show that *r*2 = 45/2𝑥. 2

[The curved surface area, *A*, of a cone with radius *r *and slant height *l *is *A *= π*rl*.] [The surface area, *A*, of a sphere with radius *r *is *A *= 4π*r*2.]

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