Question

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

Answer 1

✑ 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

Answer 2

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