The thickness of a metallic tube is 1 cm and the inner diameter of the tube is 12 cm find the weight of 1 metre long tube is the density of the metal be 7.8 gram per centimetre cube
cross section ... (π / 4)[(do)^2 - (di)^2]
volume = cross section * length
mass = volume * density
weight = m g
Area of circle:
A = d² π / 4
Inner diameter:
d1= 12 cm
Outer diameter:
d2 = d1 + 2 ∙ thickness
d2 = d1 + 2 ∙ 1 = 12 + 2 = 14 cm
Area of ring:
A = ( d2² - d1² ) ∙ π / 4
A = ( 14² - 12² ) ∙ π / 4
A = ( 196 - 144 ) ∙ π / 4
A = 52 ∙ π / 4
A = 13 π cm²
1 m = 100 cm
Volume:
V = A ∙ L
V = 13 π ∙ 100
V = 1300 π cm³
ρ = density
Weight:
w = V ∙ ρ
w = 1300 π ∙ 7.8 = 1300 ∙ 3.14159 ∙ 7.8 = 31 855.7226 gr
1kg = 1000 gr
w = 31.8557226 kg
To find the weight of the metallic tube, we need to calculate the volume of the tube first, and then multiply it by the density to get the weight.
The volume of a cylindrical tube can be calculated using the formula: V = πr^2h, where V is the volume, r is the radius, and h is the height (or length) of the tube.
In this case, the inner diameter of the tube is given as 12 cm. To find the radius (r), we divide the diameter by 2:
r = 12 cm / 2 = 6 cm
The thickness of the tube is given as 1 cm. Therefore, the outer radius (R) can be found by adding the thickness (t) to the inner radius (r):
R = r + t = 6 cm + 1 cm = 7 cm
Now that we have the outer radius, we can find the volume of the tube per centimeter:
v_cm = π(R^2 - r^2) = π(7^2 - 6^2) = π(49 - 36) = π(13) ≈ 40.84 cm^3
Since the length of the tube is given as 1 meter, the volume of a 1-meter-long tube would be:
v_1m = v_cm * 100 = 40.84 cm^3 * 100 = 4084 cm^3
Now, we can calculate the weight (W) of the tube by multiplying the volume (V) by the density (D):
W = V * D = 4084 cm^3 * 7.8 g/cm^3 ≈ 31,879.2 grams
Therefore, the weight of the 1-meter-long tube would be approximately 31,879.2 grams.