Question

How many solid right circular cylinders of radius 2 cm and height 3 cm can be made by melting a solid right circular cylinder of diameter 12 cm and height 15 cm?

Answer 1

V_cyl = πr²h

Small Cylinders

r = 2 cm, h = 3 cm

∴ `"V"_"small" = pi"r"^2"h"`

`= pi xx 2 xx 2 xx 3`  ...(i)

Big Cylinders

d = 12 cm, r' = `12/2` = 6 cm

h' = 15 cm  

∴ `"V"_"big" = pi"r'"^2"h'"`

`= pi xx 6 xx 6 xx 15`   ...(ii)

`n = "V"_"big"/"V"_"small"`   ...[From (i) and (ii)]

`= (pi xx 6 xx 6 xx 15)/(pi xx 2 xx 2 xx 3)`

= 45