Question

The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.

​

Answer 1

Given:

• Inner diameter of cylindrical wooden pipe, $\sf d_1$ = 24 cm
• Inner Radius of cylindrical wooden pipe, $\sf r_1$ = 24/2 = 12 cm
• Outer diameter of cylindrical wooden pipe, $\sf d_2$ = 28 cm
• Outer Radius of cylindrical wooden pipe, $\sf r_2$ = 28/2 = 14 cm
• Length or height of wooden pipe, h = 35 cm
• Mass of 1 cm³ wood = 0.6 g

⠀⠀⠀⠀

To find:

• Mass of pipe?

⠀⠀⠀⠀

Solution:

⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

$:\implies{\sf{\pink{Volume_{\:(pipe)} = Volume_{\;(outer\:cylinder)} - Volume_{\;(inner\:cylinder)}}}}$

$:\implies\sf Volume_{\:(pipe)} = \pi {(r_2)}^2 h - \pi {(r_1)}^2 h$

$:\implies\sf Volume_{\:(pipe)} = \pi h( {r_2}^2 - {r_1}^2)$

$:\implies\sf Volume_{\:(pipe)} = \dfrac{22}{7} \times 35 \bigg( {14}^2 - {12}^2 \bigg)$

$:\implies\sf Volume_{\:(pipe)} = \dfrac{22}{ \cancel{7}} \times \cancel{35} \times (14 - 12)(14 + 12)$

$:\implies\sf Volume_{\:(pipe)} = 22 \times 5 \times 2 \times 26$

$:\implies{\underline{\boxed{\frak{\purple{Volume_{\:(pipe)} = 5720\:cm^3}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Volume\:of\: cylindrical\:wooden\: pipe\:is\: \bf{5720\:cm^3}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

Now, Given that,

⠀⠀⠀⠀

$\dashrightarrow\sf Mass\:of\:1\:cm^3\:volume = \bf{0.6\:g}$

$\therefore\:\sf Mass\:of\:5720\:cm^3\:volume = (5720 \times 0.6)\:g$

$\qquad\qquad\qquad\implies\sf \bigg( \dfrac{5720 \times 0.6}{1000} \bigg)\:kg$

$\qquad\qquad\implies{\underline{\boxed{\frak{\pink{Mass_{\:(pipe)} = 3.432\:kg}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Mass\:of\:wooden\:pipe\:is\: {\textsf{\textbf{3.432\:kg}}}.}}}$

Answer 2

Refers to the Attachment

Hope it helps

#NAWABZAADI