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

?

Accepted Answer

Radius of big right circular triangle $= \frac{12}{2} = 6 cm$

Height of big right circular cylinder $= 15 cm$

Therefore, volume of big cylinder $= π r^{2} h$

$= \frac{22}{7} \times 6 \times 6 \times 15$

$= \frac{11880}{7} {cm}^{3}$

Since, radius and height of small cylinder is $2 cm$ and $3 cm$ respectively

Therefore, volume of one small cylinder $= π r^{2} h$

$= \frac{22}{7} \times 2 \times 2 \times 3$

$= \frac{264}{7} {cm}^{3}$

No. of small cylinder can be made $=$ Volume of cone/volume of one cylinder

$= \frac{\frac{11880}{7}}{\frac{264}{7}}$

$= 45$ cylinders

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?

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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 $15 cm$ ?