A solid iron cuboidal block of dimensions 4.4 m $ imes$ 2.6 m $ imes$ 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

Question

A solid iron cuboidal block of dimensions 4.4 m $	imes$ 2.6 m $	imes$ 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

Accepted Answer

Step 1: Internal radius of cylinder $(r_1) = 30$ cm $= 0.30$ m. Outer radius of cylinder $(r_2) = 30 + 5 = 35$ cm $= 0.35$ m
Step 2: Therefore $4.4 	imes 2.6 	imes 1 = \pi 	imes h 	imes (0.35^2 - 0.30^2)$
Step 3: $= \pi 	imes h 	imes \frac{100 	imes 100}{65 	imes 5} \Rightarrow h = \frac{352}{\pi}$ m or 112 m

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