Question

Acircular pipe is 30 cm long. Its internal and external diameters
are 5 cm and 6 cm respectively. Find the volume of material used in
making the pipe. Also find the total surface area of the pipe.​

Answer 1

Answer :-

• Volume of pipe (Material) = 259.05 cm³
• TSA of pipe = 1053.47 cm²

Given :-

• Length of pipe = 30 cm
• Internal radius (r) = 5/2 = 2.5 cm
• External radius (R) = 6/2 = 3 cm

To Find :-

• Volume of pipe (Material) = ?
• TSA of pipe = ?

Explanation :-

As above given, we have to find the TSA and volume of material of pipe. So let's find !! :)

✦ Finding volume of material of pipe,

$\blue { \boxed { \bf \bigstar \: Volume \: of \: pipe \: Material = \pi h (R^2 - r^2) \: \bigstar }}$

$\rm : \; \leadsto 3.14 \times 30 \times [(3^2)-(2.5^2)] \: \; \; cm^3$

$\rm : \; \leadsto 3.14 \times 30 \times (9-6.25) \: \; \; cm^3$

$\rm : \; \leadsto 3.14 \times 30 \times 2.75 \: \; \; cm^3$

$\rm : \; \leadsto 94.2 \times 2.75 \: \; \; cm^3$

$\red { \underline { \boxed { \bf : \; \leadsto 259.05 \: \; \; cm^3 }}}$

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✦ Finding TSA of pipe,

$\blue { \boxed { \bf \bigstar \: TSA \: of \: pipe = 2 \pi (R+r) (R-r +h) \: \bigstar }}$

$\rm : \; \leadsto 2 \times 3.14 (3 + 2.5) \times (3-2.5 + 30) \; \; \; cm^2$

$\rm : \; \leadsto 6.28 (5.5) \times (0.5 + 30) \; \; \; cm^2$

$\rm : \; \leadsto 6.28 \times 5.5 \times 30.5 \; \; \; cm^2$

$\rm : \; \leadsto 34.54 \times 30.5 \; \; \; cm^2$

$\red { \underline { \boxed { \bf : \; \leadsto 1053.47 \; \; \; cm^2 }}}$

Hence, the Volume of material of pipe and TSA of pipe are 259.05 cm³ and 1053.47 cm²