A hollow metal pipe whose internal and external diameter are 2.8cm and 6.3cm respectively is 3.5 long. a) calculate the volume of the metal used to make the pipe in cm3
wrong again!
3.5π(3.15^2 - 1.4^2) = 67.5 cm^3
Wrong again, the robot tutor was not even close
outer radius = 3.15
inner radius = 1.4
volume of material of pipe = π (3.15^2 - 1.4^2)(3.5)
= 87.55 cm^3
I assumed the 3.5 was 3.5 cm, the units were not given
To calculate the volume of the metal used to make the pipe, we need to find the difference in volumes between the outer and inner cylinders.
1. Calculate the volume of the outer cylinder:
The formula to calculate the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
The radius of the outer cylinder (R) is half of the external diameter, so R = 6.3cm / 2 = 3.15cm.
The height (h) of the cylinder is given as 3.5cm.
Therefore, the volume of the outer cylinder is V_outer = π(3.15cm)^2 * 3.5cm.
2. Calculate the volume of the inner cylinder:
The radius of the inner cylinder (r) is half of the internal diameter, so r = 2.8cm / 2 = 1.4cm.
The height (h) of the inner cylinder is the same as the outer cylinder, which is 3.5cm.
Therefore, the volume of the inner cylinder is V_inner = π(1.4cm)^2 * 3.5cm.
3. Calculate the volume of the metal used to make the pipe:
The volume of the metal used to make the pipe is the difference between the volumes of the outer and inner cylinders:
V_metal = V_outer - V_inner
Substitute the values we calculated:
V_metal = π(3.15cm)^2 * 3.5cm - π(1.4cm)^2 * 3.5cm.
Simplify the equation using the value of π and perform the calculations to get the final answer.
Note: Remember to convert the units to cm^3 because the calculations were done using centimeters.