Question : A cylindrical tube, open at both ends, is made of a metal sheet which is 0.5 cm thick. Its outer radius is 4 cm and its length is 2 m. How much metal (in cm$^3$) has been used in making the tube?
Option 1: $800 \pi$
Option 2: $450 \pi$
Option 3: $750 \pi$
Option 4: $550 \pi$
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Correct Answer: $750 \pi$
Solution :
Given: Outer radius $(R)$ = 4 cm
Thickness = 0.5 cm
Internal radius $(r)$ = 4 – 0.5 = 3.5 cm
Volume of material = $\pi(R^2 - r^2)h$
= $\pi \times (4^2 - 3.5^2)\times 200$
= $\pi \times 3.75\times 200$
= $750\pi$ cm$^3$
Hence, the correct answer is $750\pi$.
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