Question

Find the number of solid cylindrical structures of 6 radius 7 cm and height 10 cm which cane be made from a solid cylinder of radius 7 m and height 10 m

Answer 1

1000000 cylinders of radius 7 cm and height 10 cm which can be made from solid cylinder of radius 7m and height 10 m .

Solution:

Volume of cylinder is given by:

volume = $\pi r^{2} h$  where "r" is radius and "h" is height

Let us find the volume of bigger cylinder which is a solid cylinder of radius 7 m and height 10 m

$\text { Volume of bigger cylinder }=\mathrm{V}_{\mathrm{b}}=\pi r^{2} h$

Here radius = 7m = 700 cm

Height = 10m = 1000 cm

By substituting the values, we get

$\mathrm{V}_{\mathrm{b}}=\pi \times 700^{2} \times 1000=49 \pi \times 10^{7} \mathrm{cm}^{3}$

Now let us find the volume of smaller cylinder which has radius 7cm and height 10 cm

$\text { Volume of smaller cylinder }=\mathrm{V}_{\mathrm{s}}=\pi r^{2} h$

$\mathrm{V}_{\mathrm{s}}=\pi \times 7^{2} \times 10=49 \pi \times 10^{1} \mathrm{cm}^{3}$

So number of small cylinders which can be made by bigger cylinder = $\frac{V_{b}}{V_{s}}$

$=\frac{49 \pi \times 10^{7}}{49 \pi \times 10^{1}}=10^{6}=1000000$

Hence 1000000 cylinders of radius 7 cm and height 10 cm which can be made from solid cylinder of radius 7m and height 10 m .