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Question
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
Solution
Radius of a solid cone (r) = 5 cm
Height of the cone = 8 cm
Volume of a cone
= `1/3pir^2h`
= `1/3 xx 5 xx 5 xx 8 cm^3`
= `(200pi)/3 cm^3`
Radius of each sphere = 0.5 cm
∴ Volume of one sphere = `4/3pir^3`
= `4/3 xx II xx 1/2 xx 1/2 xx 1/2 cm^3`
= `(II)/6 cm^3`
Number of spheres = `"Total volume"/"Volume of one sphere"`
= `((200pi)/3)/(pi/6) xx 6/pi`
= `(200pi)/3 xx 6/pi`
= 400
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