A cylindrical casting of height 8cm and external and internal diameters 9cm and 5cm respectively. Calculate the volume of metal in the casting
The radius of the external diameter is 4.5 cm and the radius of the internal diameter is 2.5 cm.
The volume of metal in the casting can be found by subtracting the volume of the inner cylinder from the volume of the outer cylinder.
Volume of outer cylinder = π × r^2 × h = π × (4.5 cm)^2 × 8 cm = 254.47 cm^3
Volume of inner cylinder = π × r^2 × h = π × (2.5 cm)^2 × 8 cm = 157.08 cm^3
Volume of metal in casting = Volume of outer cylinder - Volume of inner cylinder
= 254.47 cm^3 - 157.08 cm^3
= 97.39 cm^3
Therefore, the volume of metal in the casting is 97.39 cm^3.
To calculate the volume of metal in the casting, we can find the difference between the volumes of the outer and inner cylinders.
The volume of a cylinder can be calculated using the formula:
V = π * r^2 * h
Where:
V = Volume
π = Pi (approximately 3.14)
r = Radius
h = Height
First, let's calculate the volume of the outer cylinder:
Radius (r) = Diameter / 2 = 9cm / 2 = 4.5cm
V_outer = π * (4.5cm)^2 * 8cm
Next, let's calculate the volume of the inner cylinder:
Radius (r) = Diameter / 2 = 5cm / 2 = 2.5cm
V_inner = π * (2.5cm)^2 * 8cm
Now, we can find the volume of the metal in the casting by subtracting the volume of the inner cylinder from the volume of the outer cylinder:
Volume of metal = V_outer - V_inner
Volume of metal = π * (4.5cm)^2 * 8cm - π * (2.5cm)^2 * 8cm
Simplifying, we have:
Volume of metal = 8π * (4.5cm)^2 - 8π * (2.5cm)^2
Volume of metal = 8π * 20.25cm^2 - 8π * 6.25cm^2
Finally, we can calculate the value by evaluating the expression:
Volume of metal ≈ 406.08 cm^3 (rounded to two decimal places)