The adjoining figure shows the cross-section of an ice cream consisting of a cone surmounted by a hemisphere. The radius of the hemisphere is 3.5 cm. and the height of the cone is 10.5 cm. The outer shell ABCDFE is shaded and is not filled with ice cream. AE = DC = 0.5 cm, AB|| EF and BC || FD. Calculate (i)The volume of the ice cream in the cone (the unshaded portion including the hemisphere in cubic cm, and (ii)The volume of the outer shell (the shaded portion') in cubic cm. Give answers correct to the nearest cubic cm.
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Volume of a cone=(1/3)(pi)r²h.
total volume of ice cream=volume of cone + volume of hemisphere
∴volume of cone=(1/3)(22/7)(3.5)²(12.5)
=(22/21)(12.25)(12.5)
=(22/21000)(1225 x 125)
=(11 x 245 x 5)/84
=13475/84.
volume of hemisphere=2/3 x (pi) x r
=2/3 x 22/7 x 3.5
=44/6
∴volume of ice cream =14091/84 cm³.
total volume of ice cream=volume of cone + volume of hemisphere
∴volume of cone=(1/3)(22/7)(3.5)²(12.5)
=(22/21)(12.25)(12.5)
=(22/21000)(1225 x 125)
=(11 x 245 x 5)/84
=13475/84.
volume of hemisphere=2/3 x (pi) x r
=2/3 x 22/7 x 3.5
=44/6
∴volume of ice cream =14091/84 cm³.
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