Question

39. The volume of a metallic cylindrical pip
is 770 cm. Its length is 14 cm and its
external radius is 9 cm. Then, its
thickness is​

Answer 1

Given :

• Volume of the hollow cylindical pipe = 770 cm³
• Length of the cylindrical pipe = 14 cm
• External radius of the cylindrical pipe = 9 cm

To Find :

• Thickness

Solution :

Volume of a hollow cylinder is given by ,

$\\ \star \: {\boxed{\purple{\sf{Volume_{(hollow \: cylinder) } = \pi( {R}^{2} - {r}^{2})h }}}}$

Here ,

• R is external radius
• r is inner radius
• h is height

We have ,

• R = 9 cm
• h = 14 cm
• V = 770 cm³

Substituting the values ;

$\\ : \implies \sf \: 770 = \dfrac{22}{7} ( {9}^{2} - {r}^{2} )14$

$\\ : \implies \sf \: 770 = \dfrac{22}{7} (81 - {r}^{2} )14$

$\\ : \implies \sf \: 770 = 22 \times 2(81 - {r}^{2} )$

$\\ : \implies \sf \: 770 = 44(81 - {r}^{2} )$

$\\ : \implies \sf \: 81 - {r}^{2} = \dfrac{770}{44}$

$\\ : \implies \sf \: 81 - {r}^{2} = 17.5$

$\\ : \implies \sf \: - {r}^{2} = 17.5 - 81$

$\\ : \implies \sf \: - {r}^{2} = - 63.5$

$\\ : \implies \sf \: r = \sqrt{63.5}$

$\\ : \implies{\underline{\boxed{\red{\mathfrak{r = 7.96 \: cm}}}}}$

Now , Thickness of a hollow cylinder is given by ;

$\\ \star \: {\boxed{\purple{\sf{thickness_{(hollow \: cylinder)} = R - r}}}}$

$\\ : \implies \sf \: thickness_{(cylindrical \: pipe)} = 14 - 7.96 \:$

$\\ : \implies{\underline{\boxed {\pink{\mathfrak{thickness_{(cylindrical\: pipe)} = 6.04 \: cm}}}}} \: \bigstar$

Hence ,

• The thickness of the given hollow cylinder 6.04 cm.

Answer 2

Given :-

Volume of pipe = 770 cm

Length of pipe = 14 cm

External Radius = 9 cm

To Find :-

Thickness

Solution :-

$\bf \: volume = \pi (R { }^{2} - {r}^{2} )h$

$\tt \: 770 = \dfrac{22}{7} \times (9 {}^{2} - {r}^{2} ) \times 14$

$\tt \: 770 = 22 \times (81 - {r}^{2} ) \times 2$

$\tt770 = 44 \times (81 - {r)}^{2}$

$\tt \: 81 - {r}^{2} = \dfrac{770}{44}$

$\tt \: 81 - {r}^{2} = 17.5$

$\tt \: - {r}^{2} = 17.5 - 81$

$\tt \: - {r}^{2} = - 63.5$

$\tt \: {r}^{2} = 63.5$

$\tt \: r = \sqrt{63.5}$

$\frak \pink{ \: r = 7.96 \: cm}$

Now,

Let's find Thickness

$\bf \: Thickness = R - r$

$\tt \: Thickness = 14 - 7.96$

$\tt \: Thickness = 6.04$