If a figure shows a cylindrical casting of height 8cm and external and internal diameters 9cm and 5cm respectively. Calculate the volume of metal in the casting
Impossible
To calculate the volume of metal in the casting, we need to determine the volume of the cylinder and subtract the volume of the hollow portion.
First, let's calculate the volume of the entire cylinder:
The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.
In this case, the external diameter is given as 9cm, so the radius (r) of the base is half of that, which is 9cm / 2 = 4.5cm.
The height (h) of the cylinder is given as 8cm.
Using the formula, the volume of the entire cylinder (Vcylinder) is:
Vcylinder = πr^2h
= π(4.5cm)^2 * 8cm
Now, let's calculate the volume of the hollow portion of the cylinder:
The hollow portion can be considered as a smaller cylinder subtracted from the larger cylinder.
The internal diameter is given as 5cm, so the radius (r_hollow) of the hollow portion is half of that, which is 5cm / 2 = 2.5cm.
Using the same height (h = 8cm), the volume of the hollow portion (Vhollow) is given by:
Vhollow = πr_hollow^2h
= π(2.5cm)^2 * 8cm
Finally, we subtract the volume of the hollow portion from the volume of the entire cylinder to get the volume of the metal in the casting:
Vmetal = Vcylinder - Vhollow
By substituting the values and performing the calculations, you can find the volume of metal in the casting.
Imagine a solid cylinder with diameter of 9 cm
Its volume would be π(4.5)^2 (8)
Now remove a cylinder with diameter 5 cm
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