5. A small solid metallic sphere has a radius of 5 cm. Calculate: (i) the volume of the sphere in terms of π (ii) the total surface area of the sphere in terms of π . Eight of these small spheres, each of radius 5 cm, are melted down and recast to form one large sphere. (iii) Calculate the radius of the large sphere.


(iv) Don states that the surface area of the large sphere will be the same as eight times the surface area of one of the small spheres. Is he correct? Justify your answer, showing all work.


6. A cylinder of diameter 16 cm contains some water. How many steel ball bearings (spheres) of diameter 6 cm must be added to the cylinder and completely submerged so that the water level rises by 9 cm?


7. A spherical fi sh tank of diameter 40 cm is half full of water. (i) Calculate the volume of water in the fi sh tank in terms of π .


The water is transferred into a new spherical tank so that the water fi lls the new tank completely. (ii) Calculate the radius of the new tank to two decimal places. (iii) Calculate the surface area of the new tank to the nearest whole number.


(iv) Ben thinks that because the volume of the larger sphere is twice the volume of the smaller sphere, then the surface area of the larger sphere will be twice the surface area of the smaller sphere. Is he correct? Justify your answer with supporting work.


8. The diagram shows two cylinders, A and B. The two cylinders have the same volume.


The radius of A is r and the radius of B is 2r . Find the height of B, in terms of h .


r A h 2r B ?


9. Water is being pumped, at a constant rate, into an underground storage tank that has the shape of a cylinder. Which of the graphs A–D best represents the change in the height of water in the tank as time passes? Justify your answer.


A B


Time


Time


C


D


Time


Time


268


Linking Thinking 2


Height


Height


Height


Height


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