The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm

Question

Q) The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the used in making the cylinder is 176 cm³, find the outer and inner radii of the cylinder.

Sapling Academy · Accepted Answer

Let's draw the diagram for the given question: 
Here, Cylinder has outer radii as $R_o$ and inner radii as $R_i$, height 14 cm.
We know that the volume of the Cylinder, $V_c = \pi (r)^2 h$
Given that h = 14 cm
Here, outer volume $V_o = \pi (R_o)^2 (14)$
And  Inner volume $V_i = \pi (R_i)^2 (14)$
From the diagram, it is clear that the difference of the outer and inner volume is the volume of the metal. It is given that metal volume is 176 cm 3
Therefore, $\pi (R_o)^2 (14) - \pi (R_i)^2 (14) = 176$
$\Rightarrow \pi (14) [(R_o)^2 - (R_i)^2] = 176$
$\Rightarrow \frac{22}{7}(14) [(R_o + R_i)(R_o - R_i)] = 176$
Given that $R_o - R_i = 1$ ......... (i)
$\Rightarrow 44[(R_o + R_i)(1)] = 176$
$\Rightarrow (R_o + R_i) = 4$ ..... (ii)
By adding Equation (i) and (ii), we get:
$(R_o - R_i) + (R_o + R_i) = 1 + 4$
$ 2 R_o = 5$
$ R_o = \frac{5}{2}$
Substituting value of $R_o$ in equation (ii), we get:
$R_o + R_i = 4$
$\Rightarrow \frac{5}{2} + R_i = 4$
$\Rightarrow R_i = 4 - \frac{5}{2}$
$\Rightarrow R_i = \frac{3}{2}$
Therefore, the outer radii of cylinder is $\frac{5}{2}$ cm and inner radii is $\frac{3}{2}$ cm.

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