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Challenge 318: Completely submerged?

Thanks to Misha, Y12, for the original version of this problem.

Dr Reasoner is constructing a water feature for her garden. It is made from a transparent cylindrical container and two metallic spheres, one with diameter 10cm and the other with diameter 14cm. The diameter of the container is 22cm. The cylinder should then be filled with water, to cover the spheres.

She places the spheres into the container and then pours in 5 litres of water.

Is this enough water to cover the spheres completely? Explain your answer clearly.

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