Question

$\huge\sf\fbox\purple{ Question }★$

°° The external diameter of a 35-cm-long metal pipe is 10 cm. If the pipe is 1 cm thick and the density of the metal is 7.8 g/cm^3, find the volume of the metal used in the pipe and the mass of the pipe.°°


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Answer 1

Answer:

$\tt 7.722 \: kg$

Step-by-step explanation:

$\sf \large \red{Given:-}$

$\tt Height= 35\:cm$

$\tt Thickness = 1\: cm$

$\tt Densiy = 7.8\: \: g/cm^3$

$\tt External \: diameter = 10 \: cm$

$\tt External\: radius = 5\: cm$

$\tt Internal \: radius = 5-1=4\: cm$

$\boxed{\rm Volume= π(R^2-r^2)h}$

$\tt : \implies \dfrac{22}{7} ×(5^2-4^2)×35$

$\tt : \implies \dfrac{22}{7} ×(25-16)×35$

$\tt : \implies \dfrac{22}{7} ×9×35$

$\tt : \implies \dfrac{22}{\cancel{7}} ×9×\cancel{35} \: \: \: 5$

$\tt : \implies 22×9×5$

$\tt : \implies 990 \: cm^3$

$\boxed{\rm Mass = Density×Volume}$

$\tt = 7.8×990$

$\tt = 7722 \: g$

$\tt = 7.722 \: kg$

Answer 2

Given :-

Height = h = 35 cm

Thickness of pipe = 1 cm

Density of material = d = 7.8 g cm-³

External diameter of pipe = D = 10 cm

External radius of pipe = R = 5 cm

Internal radius = r = External radius - Thickness

r = 5 - 1 = 4 cm

First of all we are required to find out the volume of pipe.

Volume = V = Effective Area × Height

V = π(R² - r²) h

V = 22/7 × (5² - 4²) × 35

V = 22 × 5 × 9

\bf{V\:=\:990\:{cm}^{3}}V=990cm

3

Now, We have to find out the Mass of material and we are given the density of material and from this we know a relation :-

Mass = Density × Volume

M = 7.8 × 990

M = 7722 g

M = 7.722 Kg

Hence,

Hence, The mass of material = M = 7.722 Kg✅