A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm. The metal every where is 0.4 cm thick. Calculate the volume of the metal correct to 1 place of decimal
To calculate the volume of the metal, we need to subtract the volume of the hollow space inside the tube from the volume of the outer cylindrical shape.
First, let's calculate the volume of the outer cylindrical shape:
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Given that the internal diameter of the tube (which is equal to twice the radius) is 11.2 cm, the radius (r) of the outer cylinder is half of this value: 11.2 cm / 2 = 5.6 cm.
The length (h) of the cylinder is given as 21 cm.
Plugging these values into the formula, we have:
V_outer = π(5.6 cm)^2 * 21 cm
Now, let's calculate the volume of the hollow space inside the tube:
The inner diameter of the tube is equal to the external diameter minus twice the metal thickness. Therefore, the inner diameter is 11.2 cm - 2 * 0.4 cm = 10.4 cm.
Similarly, the radius (r_inner) of the inner cylinder is 10.4 cm / 2 = 5.2 cm.
The volume of the hollow space can be calculated using the same formula:
V_inner = π(5.2 cm)^2 * 21 cm
Now we can calculate the volume of the metal by subtracting the volume of the hollow space from the volume of the outer shape:
V_metal = V_outer - V_inner
After calculating the values for V_outer and V_inner, subtract V_inner from V_outer to find the volume of the metal.
Finally, round the volume of the metal to one decimal place according to the specifications mentioned.