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प्रश्न
A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
उत्तर
Height of solid cone (h) = 8 cm
Radius (r) = 6 cm
Volume of solid cone = `1/3pir^2h`
= `1/3 xx pi xx 6 xx 6 xx 8`
= 96π cm3
Height of smaller cone = 2 cm
And radius = `1/2` cm
Volume of smaller cone
= `1/3 xx pi xx 1/2 xx 1/2 xx 2`
= `1/6pi cm^3`
Number of cones so formed
= `(96pi)/(1/6pi)`
= `96pi xx 6/pi`
= 576
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