A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21cm and its volume is 2/3 of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy. `(U s epi=(22)/7)dot`

Explanation

Given: Radius of base of con` r=21`

And volume of cone` = ⅔` volume of hemisphere

`:. 1/3 pi r^2 h = 2/3 ( 2/3 pi r^3)`

`:. h= 4/3 r = (4xx21)/3 = 28cm`

Slant height` l^2 = r^2 + h^2`

`:. l^2 = 21^2 + 28^2`

`:. l = 35cm`

Total surface area = surface are of cone + surface area of hemisphere

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