Question

An ink container of cylindrical shape is filled with ink up 91%. Ball pen refils of length 12 cm and inner diameter 2 mm are filled upto 84%. If the height and radius of the ink container are 14 cm and 6 cm respectively, find the number of refils that can be filed with this ink.

Answer 1

Given:
Length of the refill = 12 cm
Inner diameter of the refill = 2 mm
∴ Inner radius of refill = $\frac{2}{2}$ mm = 1 mm = 0.1 cm
Now,
Volume of one refill = $\mathrm{\pi }$r²h
= $\frac{22}{7}\times (0.1{)}^2\times 12$
= 0.377 cm³
Because the refills are filled up to 84%, the volume of the ink filled in each refill is:
$\frac{84}{100}\times 0.377$ cm³
= 0.3166 cm³
Also,
Height of the container = 14 cm
Radius of the container = 6 cm
Now,
Volume of the container = $\mathrm{\pi }$r²h
= $\frac{22}{7}\times 6^2\times 14$
= 1584 cm³
Because the container is filled with ink up to 91%, the volume of the ink filled in the container is:
$\frac{91}{100}\times 1584$ = 1441.44 cm³
Thus, we have:
Number of refills that can be filled = $\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{ink}\mathrm{filled}\mathrm{in}\mathrm{the}\mathrm{container}}{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{ink}\mathrm{filled}\mathrm{in}\mathrm{each}\mathrm{refill}}$
= $\frac{1441.44}{.3166}$

= 4552.87

Hence, the number of refills that can be filled is 4552.