Question

plz help me tell me my question
the difference between the inner and outer surface area of cylindrical pipe is 88 cmsquare . if the height of the cylindrical pipe is 14 cm and volume is 176 cm cube,find the inner and outer radii of pipe. plz ​

Answer 1

AnswEr :

• Difference between Inner and Outer Surface Area is 88 cm²
• Height of Cylindrical Pipe is 14 cm
• Volume of Cylindrical Pipe is 176 cm³

Let's the Inner Radius be r and, Outer Radius be R of Cylindrical Pipe.

• Let's Head to the Question Now :

$\longrightarrow \tt Outer \:Surface \: Area - Inner \:Surface \:Area = 88 \:{cm}^{2} \\ \\\longrightarrow \tt2\pi h(R - r) = 88 \:{cm}^{2} \\ \\\longrightarrow \tt2 \times \dfrac{22}{\cancel7}\times \cancel{14}(R - r) = 88 \\ \\\longrightarrow \tt2 \times 22 \times 2(R - r) = 88 \\ \\\longrightarrow \tt(R - r) = \cancel\dfrac{88}{2 \times 22 \times 2} \\ \\\longrightarrow \tt(R - r) = 1 \\ \\\longrightarrow \green{\tt R = 1 + r}$

$\rule{300}{1}$

• According to the Question Now :

$\implies \tt Volume \:of \:Pipe = \pi h({R}^{2} - {r}^{2}) \\ \\\implies \tt 176 {cm}^{3} = \pi h({(1 + r)}^{2} - {r}^{2}) \\ \\\implies \tt 176 = \dfrac{ 22}{ \cancel7} \times \cancel{14} \times(1 + r + r) \times(1 \cancel{+ r - r}) \\ \\\implies \tt 176 = 22 \times2 \times(1 + 2r) \times 1 \\ \\\implies \tt \cancel\dfrac{176}{22 \times 2} =1 + 2r \\ \\\implies \tt4 = 1 + 2r \\ \\\implies \tt \dfrac{(4 - 1)}{2} = r \\ \\\implies \blue{\tt r = 1.5 \: cm}$

$\rule{300}{1}$

• O U T E R ⠀R A D I U S :

⇒ R = 1 + r

⇒ R = 1 + 1.5 cm

⇒ R = 2.5 cm

⠀

∴ Inner and Outer Radius of Cylindrical Pipe is 1.5 cm and 2.5 cm respectively.

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