Question

An iron pipe is 20 cm long, and has exterior diameter equal to 25 cm. if the thickness of the pipe is 1 cm. find the total surface area of the pipe.​

Answer 1

✯ $\huge\underline\mathbb{ANSWER}$

The total surface area of the pipe is 3168 cm² .

• ${\underline{\bf{Given\::}}}$

Length of pipe = 20 cm

Outer Diameter = 25 cm

The thickness of Pipe = 1 cm

• ${\underline{\bf{To\:find\::}}}$

Total Surface Area of the pipe = ?

✯ $\huge\underline\mathbb{SOLUTION}$

Length of pipe = 20 cm

Inner diameter = 25 - (1 + 1)

= 23 cm

Inner radius = 23/2 = 11.5 cm

Now,

Let the external radius be R and the internal radius be r.

Total surface area of the pipe = 2πh(R + r) + 2π(R² - r²)

Substituting the values in the above formula, we get,

⇒ 2*22/7*20(12.5 + 11.5) + 2*22/7*{(12.5)² - (11.5²)

⇒ (44*480)/7 + (44*24)/7

⇒ 21120/7 + 1056/7

⇒ 22176/7

= 3168 cm²

Thus, the total surface area of the pipe is 3168 square cm.

Answer 2

❥${\purple{\underline{\underline{\large{\mathtt{ANSWER:-}}}}}}$

Total surface area is 3168 cm².

❥${\purple{\underline{\underline{\large{\mathtt{EXPLANATION:-}}}}}}$

•Given:-

• Height of iron pipe= 20 cm.
• Exterior diameter = 25 cm.
• Thickness of pipe = 1 cm.

•To find:-

• Total surface area of pipe.

• Solution:-

Exterior diameter = 25 cm.

${\boxed{\sf{\green{Exterior\: radius=\frac{Exterior\: diameter}{2}}}}}$

So, exterior radius (r)=25/2=12.5 cm

Thickness = 1 cm.

So, interior radius(r') = (12.5 - 1) cm

= 11.5 cm

We know,

${\boxed{\sf{\blue{ Total\: surface\: area\:=\:2\pi(r+r')h+2\pi(r^2-r'^2)}}}}$

${\sf{\orange{Total\: surface\: area\::}}}$

${\sf{2\pi(r+r')h+2\pi(r^2-r'^2)}}$

${\sf{→2×\frac{22}{7}[(12.5+11.5)×20+(12.5^2-11.5^2)]\:cm^2}}$

${\sf{→2×\frac{22}{7}×(480+24)\:cm^2}}$

${\sf{→2×\frac{22}{7}×504\:cm^2}}$

${\sf{→2×22×72\:cm^2}}$

${\sf{→3168\:cm^2}}$

Total surface area is 3168 cm².