Question

The Difference between outside and inside surfaces of a cylindrical metallic pipe 14 cm long is 44 cm. If the pipe is made of 99cu.cm of metals. Find the outer and inner radii of the pipe

Answer 1

Answer:

Let R and r cm be the external and internal radii of the metallic pipe.

We have, h = length of the pipe is = 14 cm.

Now,

Outside surface area - inside surface area = 44 cm²

$\rightarrow \: \tt \: 2\pi Rh \: - 2\pi rh = 44 \\ \\ \rightarrow \tt \: 2\pi(R - r)h = 44 \\ \\ \rightarrow \tt \: 2 \times \frac{22}{7} (R - r) \times 14 = 44 \\ \\ \rightarrow \tt \: R - r = \frac{1}{2}$

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It is given that the volume of the metal used = 99 cubic centimetres

$\therefore$ External volume - internal volume = 99 cubic centimetres

$\rightarrow \tt \: \pi {R}^{2} h - \pi {r}^{2} h = 99 \\ \\ \rightarrow \tt \: \pi( {R}^{2} - {r}^{2} )h = 99 \\ \\ \rightarrow \tt \: \frac{22}{7} \times (R + r)(R - r) \times 14 = 99 \\ \\ \rightarrow \tt \: \frac{22}{7} \times (R + r) \times \frac{1}{2} \times 14 = 99 \\ \\ \rightarrow \tt \: R + r \: = \frac{99}{22} \\ \\ \rightarrow \tt \: R + r = \frac{9}{2}$

Solving, we get R = 2.5 and r = 2.

Hence, outer radius = 2.5 cm, and inner radius = 2 cm.