The cross-section of an ice-cream cone consists of a cone surmounted by a hemisphere, as shown i...

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The cross-section of an ice-cream cone consists of a cone surmounted by a hemisphere, as shown in the given figure. The radius of the hemisphere is 3.5 \( \mathrm{cm} \) and the height of the cone is \( 10.5 \mathrm{~cm} \). The outer shell ABCDFE is shaded and is not filled with icecream. \( \mathrm{AE}=\mathrm{DC}=0.5 \mathrm{~cm}, \mathrm{AB} \| \mathrm{EF} \) and \( \mathrm{BC} \| \mathrm{FD} \). Find:
i) The volume of the ice-cream in the cone (the unshaded portion including the hemisphere) in \( \mathrm{cm}^{3} \),
i) The volume of the outer shell (the shaded portion) in \( \mathrm{cm}^{3} \). Give your answer to the nearest \( \mathrm{cm}^{3} \).
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