We can deduce the relation 2 (r+h) as the surface area ofa cylinder in anotherway. Imagine cutting up a cylinder as shown below (Fig 11.40)
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Ruthwik3949
02.06.2020
Math
Secondary School
answered • expert verified
The outer and inner diameter of a hollow cylindrical pipe are 10 cm and 6 CM. If its length be 21 cm find the total curved surface and volume of the pipe
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MrInvisible
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✑ Gɪᴠᴇɴ :-
Outer Radius (R) = 10 cm
Inner Radius (r) = 6 cm
Height (h) = 21 cm
✑ ᴛᴏ ғɪɴᴅ :-
Total Surface Area (TSA)
Volume
✑ sᴏʟᴜᴛɪᴏɴ :-
We know that,
➦ Volume of hollow cylinder =
↣ (external volume ) - ( Internal volume)
↣ πR²h - πr²h
↣ πh (R² - r²)
Put the above given values in it, we get,
↣ 22/7 × 21 (10² - 6²)
↣ 22 × 3 (100 - 36)
↣ 22 × 3 × 64
↣ 4,224 cm³
Now,.
We know that,
➦ Total surface area of hollow cylinder =
↣(curved surface area)+(area of base rings)
↣ {(2πRh + 2πrh) + 2(πR² - πr²)}
↣ {(2πh (R + r) + 2π(R² - r²)}
↣ {2πh(R + r) + 2π( R + r) (R - r)}
↣ 2π(R + r) ( h + R - r)
Put the above given values in it, we get
↣ 2 × 22/7 ( 10 + 6)(21 + 10 - 6)
↣ 44/7 × 16 × (31 - 6)
↣ 44/7 × 16 × 25
↣ 17600/7
↣ 2514.28 cm²
Hence,
Total surface area = 2514.28 cm²
Volume = 4224 cm³
Step-by-step explanation: