Question

a cylinder is used to hold as many marbles as it can. The cylinder has a height of 25cm and a radius of 7cm. Each marble has a radius of 6mm. How many marbles can go into the cylinder? "How will you account for the spaces that are wasted due to the spherical shape of the marble? Apply that method to determine the most realistic number or marbles.

Answer 1

The number of marbles into the cylinder is 4253

Explanation:

Given as :

The height of cylinder = 25 cm

The radius of cylinder = 7 cm

Now, volume of cylinder =
`\pi` × r² × h

where r is the radius of the base of cylinder

And h is the height of the cylinder

So, volume of cylinder =
`\pi` × (7)² × 25

I.e volume of cylinder = 3.14 × 49 × 25

∴ volume of cylinder = 3846.5 cm³

Now, again

∵ Cylinder used to hold the marbles

And the radius of marble = 6 mm = 6 × 0.1 = 0.6 cm

So, volume of marble = volume of sphere =
`(4)/(3)`×
`\pi` × r³

Or, volume of sphere =
`(4)/(3)` × 3.14 × (0.6)³

Or, volume of sphere =
`(4)/(3)` × 3.14 × 0.216

or, volume of sphere = 0.90432 cm³

So, Number of marbles in to the cylinder =
`(\textrm volume of cylinder)/(\textrm volume of sphere)`

or, Number of marbles in to the cylinder =
`(3846.5)/(0.90432)`

Or, Number of marbles in to the cylinder = 4253.472 ≈ 4253

Hence The number of marbles into the cylinder is 4253 answer