Question

please help me friends

Answer 1

Given : The Ink Container is Cylindrical in shape

Given : The Height of the Ink Container is 14 cm

Given : The Radius of the Ink Container is 6 cm

Let us find the Volume of the Ink Container :

★  Volume of a Cylinder is given by : π × (Radius)² × (Height)

$\mathsf{\implies Volume\;of\;the\;Ink\;Container = \pi \times (6)^2 \times 14}$

$\mathsf{\implies Volume\;of\;the\;Ink\;Container = \dfrac{22}{7} \times 36 \times 14}$

$\mathsf{\implies Volume\;of\;the\;Ink\;Container = 22 \times 36 \times 2}$

$\mathsf{\implies Volume\;of\;the\;Ink\;Container = 1584\;cm^3}$

$\textsf{Given : The Ink Container is filled with Ink upto 91\%}$

$\implies \textsf{Volume of Ink in the Container = 91\% \times Volume of the Container}$

$\implies \mathsf{Volume\;of\;Ink\;in\;the\;Container = \dfrac{91}{100} \times 1584}$

$\implies \mathsf{Volume\;of\;Ink\;in\;the\;Container = 0.91 \times 1584}$

$\implies \mathsf{Volume\;of\;Ink\;in\;the\;Container = 1441.44\;cm^3}$

We know that : Ballpen refill is Cylindrical in shape

Given : The Length of the Ballpen refill is 12 cm

Given : The Inner Diameter of the Ballpen refill is 2 mm

●  As Radius is Half of the Diameter :

$\implies$  The Radius of the Ballpen refill is 1 mm

★  We know that : 1 mm = 0.1 cm

$\implies$  The Radius of the Ballpen refill is 0.1 cm

Let us find the Volume of One Ballpen refill :

$\mathsf{\implies Volume\;of\;the\;Ballpen\;refill = \pi \times (0.1)^2 \times 12}$

$\mathsf{\implies Volume\;of\;the\;Ballpen\;refill = 3.14 \times 0.01 \times 12}$

$\mathsf{\implies Volume\;of\;the\;Ballpen\;refill = 0.377\;cm^3}$

$\textsf{Given : The Ballpen refill is filled with Ink upto 84\%}$

$\implies \textsf{Volume of Ink in the Refill = 84\% \times Volume of the Refill}$

$\implies \mathsf{Volume\;of\;Ink\;in\;the\;Ballpen\;refill = \dfrac{84}{100} \times 0.377}$

$\implies \mathsf{Volume\;of\;Ink\;in\;the\;Ballpen\;refill = 0.84 \times 0.377}$

$\implies \mathsf{Volume\;of\;Ink\;in\;the\;Ballpen\;refill = 0.317\;cm^3}$

In order to solve the Problem : We need to realize that Volume of the Ink in the Container before filling in the Ballpen refills should be equal to Volume of Ink in the Total Number of refills which are filled. Because : Total Volume of the Ink remains Constant.

Let the Number of Ballpen refills filled with Ink be : R

$\implies \textsf{R \times Volume of Ink in each refill = Total Volume of Ink in the Container}$

$\mathsf{\implies R \times 0.317 = 1441.44}$

$\mathsf{\implies R = \dfrac{1441.44}{0.317}}$

$\mathsf{\implies R = 4547.13}$

$\implies \textsf{Number of refills that can be filled with Ink is : 4547 (approx)}$