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
Area of a circle = πr²
Inner diameter = 12 cm
Inner radius = 6 cm
Outer radius = 6+1 = 7 cm
Cross sectional area of an annulus (ring)
= π(r2²-r1²)
=(7²-6²)π
=13π cm²
Volume for a 1 metre tube:
V=13π&100cm cm³
=1300 cm³
Mass ("weight")
=volume * density.
To find the weight of the metallic tube, we need to consider its volume and density. Here's how to calculate it step by step:
1. First, we need to find the outer diameter of the tube. The inner diameter is given as 12 cm, and the thickness of the tube is 1 cm. The outer diameter can be obtained by adding twice the thickness to the inner diameter:
Outer diameter = Inner diameter + 2 × thickness
= 12 cm + 2 × 1 cm
= 12 cm + 2 cm
= 14 cm
2. Next, we find the volume of the tube. The formula to calculate the volume of a cylinder is:
Volume = π × (radius)^2 × height
Since we have the diameter, we need to convert it to radius by dividing it by 2:
Radius = Diameter / 2
= 14 cm / 2
= 7 cm
The height of the tube is 1 meter, which is equal to 100 cm.
Thus, the volume of the tube is:
Volume = π × (7 cm)^2 × 100 cm
= π × 49 cm^2 × 100 cm
= 4900π cm^3 (approx. 15394.24 cm^3)
3. Now we can calculate the weight of the tube using the formula:
Weight = Volume × Density
Given that the density of the metal is 7.8 g/cm^3, we have:
Weight = 15394.24 cm^3 × 7.8 g/cm^3
≈ 120044.35 g (approx. 120.04 kg)
Therefore, the weight of the 1-meter long metallic tube is approximately 120.04 kg.