A cylindrical aluminium container of height 12cm has an inner diameter of 14cm and outer diameter of 15cm calculate the volume of metal used for the container
To find the volume of metal used for the container, we need to subtract the volume of the inner cylinder from the volume of the outer cylinder.
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
First, let's calculate the radius of the inner cylinder:
Radius = inner diameter / 2 = 14cm / 2 = 7cm
Next, let's calculate the volume of the inner cylinder:
Volume_inner = π * (7cm)^2 * 12cm
Now, let's calculate the radius of the outer cylinder:
Radius = outer diameter / 2 = 15cm / 2 = 7.5cm
Next, let's calculate the volume of the outer cylinder:
Volume_outer = π * (7.5cm)^2 * 12cm
Finally, let's calculate the volume of metal used for the container by subtracting the volume of the inner cylinder from the volume of the outer cylinder:
Volume_metal = Volume_outer - Volume_inner
To calculate the volume of metal used for the container, we can subtract the volume of the inner cylinder from the volume of the outer cylinder.
Let's calculate the volume of the outer cylinder first:
The outer radius is half the outer diameter, so the outer radius = 15 cm / 2 = 7.5 cm.
The volume of a cylinder can be found using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
So, the volume of the outer cylinder is V_outer = π * (7.5 cm)^2 * 12 cm.
Now, let's calculate the volume of the inner cylinder:
The inner radius is half the inner diameter, so the inner radius = 14 cm / 2 = 7 cm.
The volume of the inner cylinder is V_inner = π * (7 cm)^2 * 12 cm.
Finally, to calculate the volume of the metal used for the container, we subtract the volume of the inner cylinder from the volume of the outer cylinder:
Volume of metal used = V_outer - V_inner.