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Question

The given figure represents a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each and the slant height of the cone is 5 cm. Calculate:
(i) the height of the cone.
(ii) the volume of the solid. [4 MARKS]

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Solution

Each Part: 2 Marks

Given: Slant height, l = 5 cm
and diameter = 6 cm
r = 3 cm

i) Let the height of cone be 'h'
Then, l2=h2+r2
52=h2+32
h=259 cm=4 cm

ii) Volume of solid = Volume of cone + Volume of hemisphere
=13πr2h+23πr3=13πr2(h+2r)
=13×227×9(4+2×3)=94.3 cm3
Volume of the metallic sphere
=43πR3=43π(7)3 cm3
Radius of the small metallic sphere
=3.52=74 cm
Volume of a small metallic sphere
=43πr3=43π(74)3 cm3


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