(Solved): a) A group of engineers want to design an underground water storage tank whic ...

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a) A group of engineers want to design an underground water storage tank which is constructed in the shape of a cylinder with a hemisphere at each end as shown below. i) Find the volume of the water storage tank. (10 marks) Give your answer with pi \( (\pi) \) (exact form). ii) Calculate the total outside surface area of the tank. (10 marks) Give your answer with pi ( \( \pi \) ) (exact form). iii) The engineers want to change the design and remove the spheres at the end and keep the cylindrical shape. They want to keep the same height of the tank. However, they want to decrease by \( \frac{16}{3} \pi \mathrm{m}^{3} \) the volume calculated in part (i). Calculate the new length (L) of the tank with the new design. (10 marks) iv) The engineers also want to know: If they keep the cylindrical shape only and the same volume of the tank as in part (iii) but with the length \( L=16 \mathrm{~m} \), what would be the new height \( (\mathrm{H}) \) of the tank? Give the exact value. v) Finally, the engineers want to know: If the tank does have a shape of sphere only (without a cylinder in the middle) and the same volume as in part (i), what would be the radius \( \mathrm{R} \) of such a spherical tank? Give the exact value. (5 marks)