the thickness of a metallic tube is 1 cm and the inner diameter of tube is 12 cm . Find the weight of 1 meter tube long, if the density of metal be 7.8 gram/cm^3
To find the weight of the tube, we need to calculate the volume of the tube first, and then multiply it by the density of the metal.
Step 1: Calculate the volume of the tube.
The volume of a hollow cylinder (like a tube) can be calculated using the formula:
Volume = π * (Outer radius^2 - Inner radius^2) * Length
Given:
Thickness of the tube = 1 cm
Inner diameter of the tube = 12 cm
Length of the tube = 1 meter (100 cm)
To find the outer radius of the tube, we can calculate it as:
Outer radius = Inner radius + Thickness = (12/2) + 1 = 6 + 1 = 7 cm
Now we can calculate the volume of the tube using the formula:
Volume = π * (7^2 - 6^2) * 100
= 3.14 * (49 - 36) * 100
= 3.14 * 13 * 100
= 4086 cm^3
Step 2: Calculate the weight of the tube.
The weight of the tube can be calculated using the formula:
Weight = Volume * Density
Given:
Density of the metal = 7.8 gram/cm^3
Weight = 4086 * 7.8 gram
= 31,858.8 gram
So, the weight of a 1-meter-long tube with a thickness of 1 cm and an inner diameter of 12 cm, made of metal with a density of 7.8 g/cm^3, is approximately 31,858.8 grams.
Area of a circle = ðr²
Inner diameter = 12 cm
Inner radius = 6 cm
Outer radius = 6+1 = 7 cm
Cross sectional area of an annulus (ring)
= ð(r2²-r1²)
=(7²-6²)ð
=13ð cm²
Volume for a 1 metre tube:
V=13ð&100cm cm³
=1300 cm³
Mass ("weight")
=volume * density.