Question

The length of a metallic tube is 1 metre, its thickness is 1 cm and its inner diameter is 12 cm. Find the weight of the tube if the density of the metal is 7.7 gram per cubic centimetre.​

Answer 1

• inner diameter = 12 cm

Therefore, radius = 6 cm

• Thickness = 1 cm

External radius = thickness + inner radius

• =1 + 6 = 7 cm.

Length of tube = 1 m = 100 cm

• Now, volume of tube = π(R² - r²)h

22/7 * (7² - 6²) * 100

22/7 * 13 * 100 = 4085.71 cm³

• Density of metal per cm³ = 7.7 g

Weight of tube = 7.7 g × 4085.71

                          = 31868.538 g

                          = 31.868 kg

Answer 2

AnswEr :

31.45 kg.

$\bf{\pink{\underline{\underline{\bf{Given\::}}}}}$

The length of a metallic tube is 1 m, it's thickness is 1 cm and it's inner diameter is 12 cm. If the density of the metal is 7.7 gram/cm³.

$\bf{\pink{\underline{\underline{\bf{To\:find\::}}}}}$

The weight of the tube.

$\bf{\pink{\underline{\underline{\bf{Explanation\::}}}}}$

$\bf{We\:have}\begin{cases}\sf{Height\:of\:tube\:=1\:m=100cm}\\ \sf{Thickness = 1cm}\\ \sf{Inner\:diameter\:=\:12\:cm}\\ \sf{Inner\:radius\:=\:\cancel{\frac{12}{2}} =6\:cm}\\ \sf{Density\:of\:metal\:=\:7.7 gram/cm^{3} }\end{cases}}$

We have outer radius (R) = r + 1

Outer radius (R) = 6 + 1 = 7 cm

$\bf{\red{\underline{\underline{\tt{A.T.Q\::}}}}}$

Formula use :

$\bf{\boxed{\bf{Volume\:of\:Cylinder\:=\:\pi r^{2} h}}}}}}$

$\mapsto\sf{Volume=\pi R^{2} h-\pi r^{2} h}\\\\\\\mapsto\sf{Volume=\pi h[R^{2} -r^{2} ]}\\\\\\\mapsto\sf{Volume=\dfrac{22}{7} \times 100\big[(7)^{2}-(6)^{2} \big]}\\\\\\\mapsto\sf{Volume=\dfrac{2200}{7} \times (49-36)}\\\\\\\mapsto\sf{Volume=(314.28\times 13)cm^{3} }\\\\\\\mapsto\sf{\pink{Volume=4085.71\:cm^{3} }}$

Now,

$\leadsto\sf{Mass=Density\times Volume}\\\\\\\leadsto\sf{Mass=7.7 gm/cm^{3} \times 4085.71cm^{3} }\\\\\\\leadsto\sf{Mass=31459.96\:gram}\\\\\\\leadsto\sf{Mass=\dfrac{31459.96}{1000} \:kilogram}\\\\\\\leadsto\sf{\pink{Mass=31.45\:kilograms}}$

$\underbrace{\sf{The\:weight\:of\:the\:tube=31.45\:kg.}}}}}$