Q.The difference between the outer and inner curved surface areas of a hollow cylindrical pipe is 44 square centimeters, and the length of the pipe is 14 cm. The volume of the material of the pipe is 99 cubic centimeters. Find the outer and inner radii of the pipe.

Here’s the English translation of the full solution: --- Let the inner radius of the pipe be \( r \) cm and the outer radius be \( R \) cm. Given height \( h = 14 \) cm According to the question: \[ 2\pi Rh - 2\pi rh = 44 \Rightarrow 2\pi h(R - r) = 44 \Rightarrow 2 × \frac{22}{7} × 14 (R - r) = 44 \Rightarrow R - r = \frac{1}{2} \quad \text{——— (i)} \] Also, \[ \pi R^2h - \pi r^2h = 99 \Rightarrow \pi h(R^2 - r^2) = 99 \Rightarrow \frac{22}{7} × 14 (R + r)(R - r) = 99 \Rightarrow 44 × (R + r) × \frac{1}{2} = 99 \Rightarrow R + r = \frac{9}{2} \quad \text{——— (ii)} \] Adding equations (i) and (ii): \[ (R - r) + (R + r) = \frac{1}{2} + \frac{9}{2} \Rightarrow 2R = \frac{10}{2} = 5 \Rightarrow R = \frac{5}{2} = 2.5 \] Substituting \( R = 2.5 \) into equation (ii): \[ R + r = \frac{9}{2} \Rightarrow 2.5 + r = 4.5 \Rightarrow r = 2 \] --- Therefore, the outer radius of the pipe is 2.5 cm and the inner radius is 2 cm.
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