Question

A metal solid cylinder has diameter 7 and length 18 .How many small

balls of 0.5 radius can be made from the cylinder?​

Answer 1

Given:-

• Diameter of solid metal cylinder is 7 units.

• Length of solid metal cylinder is 18 units.

• Radius of ball is 0.5 units.

To FInd:-

• How many balls can be made from the cylinder?

Solution:-

Here, Radius of cylinder = $\dfrac{d}{2}$

                                        = $\dfrac{7}{2}$ units

∵  Volume of Solid metal Cylinder = $\pi r^{2} h$

                                                         = $\dfrac{22}{7} \times \dfrac{7}{2} \times \dfrac{7}{2} \times 18 \ units$

                                                         = 693 unit³

Therefore, Volume of sphere ( ball ) = $\dfrac{4}{3}\pi r^{3}$

                                                              = $\dfrac{4}{3}\times \dfrac{22}{7}\times 0.5 \times 0.5 \times 0.5$

                                                              = 0.5 unit³

Now, Number of balls = $\dfrac{Volume \ of \ cylinder}{Volume \ of \ ball}$

                                     = $\dfrac{693 \ unit^{3}}{0.5 \ unit^{3}}$

                                     = 1386 balls

Hence, total number of balls formed is 1386.

Some Important Terms:-

• Volume of Hemisphere = $\dfrac{2}{3}\pi r^{3}$

• Volume of Cone = $\dfrac{1}{3}\pi r^{2} h$