A solid is in the form of a cone mounted on a hemisphere in such a way that the centre of the ba...

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A solid is in the form of a cone mounted on a hemisphere in such a way that the centre of the base of the cone just coincide with the centre of the base of the hemisphere. Slant height of the cone is \( \ell \) and radius of the base of the cone is \( 1 / 2 \mathrm{r} \), where \( \mathrm{r} \) is the radius of the hemisphere. Prove that the surface area of the solid is \( \pi / 4(11 \mathrm{r}+2 \ell) \mathrm{r} \) sq. units.
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