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 $176 \mathrm{~cm}^{3}$, find the outer and inner radii of the cylinder. This section consists of 4 questions of 5 marks each.
Explanation
Let the outer and inner radii of the cylinder be R and r respectively. Given that the difference between the outer and inner radii is 1 cm, we have R - r = 1. The volume of the metal used in making the cylinder is 176 cm^3. The volume of the metal is equal to the difference in the volumes of the outer and inner cylinders. We can write the equation as π(R^2 - r^2) * 14 = 176. Simplifying the equation, we get (R + r) * (R - r) * 14 = 176. Substituting R - r = 1, we get (R + r) * 14 = 176. Solving for R + r, we get R + r = 12.6. Since R - r = 1, we can solve for R and r. We get R = 6.8 and r = 5.8. Hence, the outer radius is 6.8 cm and the inner radius is 5.8 cm.
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