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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 metal used in making the cylinder is $176$ cm$^3$, find the outer and inner radii of the cylinder.
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Sol. Let outer radius be $r_2$ cm and inner radius be $r_1$ cm.
$\therefore r_2 - r_1 = 1$ ----- (i)
Volume of metal used = $176$ cm$^3$
$\Rightarrow \frac{22}{7} \times 14 \times (r_2^2 - r_1^2) = 176$
$\Rightarrow r_2 + r_1=4$ ----- (ii)
Solving (i) and (ii), we get
$r_2 = \frac{5}{2}$ or $2.5$, $r_1 = \frac{3}{2}$ or $1.5$
Therefore, outer radius = $2.5$ cm and inner radius = $1.5$ cm
$\therefore r_2 - r_1 = 1$ ----- (i)
Volume of metal used = $176$ cm$^3$
$\Rightarrow \frac{22}{7} \times 14 \times (r_2^2 - r_1^2) = 176$
$\Rightarrow r_2 + r_1=4$ ----- (ii)
Solving (i) and (ii), we get
$r_2 = \frac{5}{2}$ or $2.5$, $r_1 = \frac{3}{2}$ or $1.5$
Therefore, outer radius = $2.5$ cm and inner radius = $1.5$ cm