The outer and inner diameter of a hollow cylindrical pipe are 10cm and 6cm.of its length be 21cm.find the total curved surface and volume of the pipe.
Answers
Answer:
- 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
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GIVEN
The outer and inner diameter of a hollow cylindrical pipe are 10 cm and 6 CM. If its length be 21 cm .
TO FIND
Find the total curved surface and volume of the pipe
SOLUTION
Outer diameter (R) = 10cm
Inner diameter (r) = 6cm
Height (h) = 21 cm
★ Volume of cylinder
→ πR²h - πr²h
→ πh(R² - r²)
→ 22/7 × 21 × [(10)² - (6)²]
→ 22 × 3 × [(10 + 6)(10 - 6)]
→ 66 × [16 × 4]
→ 66 × 64
→ 4224 cm³
_____________________
★ Total surface area of cylinder
→ (curved surface area) + (area of base rings)
→ (2πrh + 2πRh) + (2πR² - 2πr²)
→ 2πh(r + R) + 2π(R² - r²)
→ 2×22/7 × 21(10 + 6) + 2×22/7[(10)² - (6)²]
→ 2 × 22 × 3 × 16 + 44/7[(10 + 6)(10 - 6)]
→ 44 × 48 + 44/7[16 × 4]
→ 2112 + 44/7 × 64
→ 2112 + 402.2
→ 2514.5 cm²
_____________________
Hence, volume of cylinder is 4224 cm³
and total surface area of cylinder is 2514.5 cm²
ct
Step-by-step explanation:
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★Question★
→ The outer and inner diameter of a hollow cylindrical pipe are 10cm and 6cm.of its length be 21cm.find the total curved surface and volume of the pipe.
★ Answer refer to the attachment↑↑
