A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm.

Question:

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. Then number of such cones will be
(a) 21
(b) 63
(c) 126
(d) 130

Solution:

(c)  126

Number of cones $=\frac{\text { volume of the sphere }}{\text { volume of } 1 \text { cone }}$

$=\frac{\frac{4}{3} \pi \times 10.5 \times 10.5 \times 10.5}{\frac{1}{3} \pi \times 3.5 \times 3.5 \times 3}$

$=4 \times 3 \times 3 \times 3.5=126$

 

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