A cylindrical pipe made of metal is 3cm thick.if the internal radius of the pipe is 10cm find the volume of the metal used in making 3cm in the pipe
To find the volume of the metal used in making the 3 cm thick pipe, we need to determine the volume of the outer cylinder and subtract the volume of the inner cylinder.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height or thickness.
In this case, we need to find the volume of the outer cylinder first:
1. Find the radius of the outer cylinder:
The internal radius of the pipe is given as 10 cm. Since the thickness of the pipe is 3 cm on each side, the outer radius would be the sum of the internal radius and the thickness on one side:
Outer radius (R) = Internal radius + Thickness
= 10 cm + 3 cm
= 13 cm.
2. Find the height of the outer cylinder:
Since the metal is used to make the 3 cm thick pipe, the height of the outer cylinder would be the same as the height of the pipe (h = 3 cm).
3. Calculate the volume of the outer cylinder:
V_outer = πR²h
= π(13 cm)²(3 cm)
= 507π cm³.
Next, we need to find the volume of the inner cylinder:
1. Find the height of the inner cylinder:
Since the thickness of the pipe is 3 cm, the height of the inner cylinder would be the same as the height of the pipe (h = 3 cm).
2. Calculate the volume of the inner cylinder:
The radius of the inner cylinder is the same as the internal radius of the pipe, given as 10 cm.
V_inner = π(10 cm)²(3 cm)
= 300π cm³.
Finally, we can find the volume of the metal used by subtracting the volume of the inner cylinder from the volume of the outer cylinder:
Volume of metal = V_outer - V_inner
= (507π cm³) - (300π cm³)
= 207π cm³.
Therefore, the volume of the metal used in making the 3 cm thick pipe is 207π cm³.
To get the outer radius of the cylinder you add the thickness which is 3cm,calculate differently the volume of the outer cylinder and the inner one using the formula pi×r^2×h, using 3m=300cm as the height then,subtract the volume of the inner cylinder from the outer cylinder and get the final answer.
Why did the metal pipe become an aspiring musician? Because it was trying to find its own groove!
To calculate the volume of the metal used in making the 3cm thick pipe, we need to find the difference between the volumes of the outer and inner cylinders.
The volume of the outer cylinder (with the external radius) can be calculated using the formula:
V_outer = π * (r_outer)^2 * h
where r_outer is the external radius and h is the height of the pipe.
The volume of the inner cylinder (with the internal radius) can be calculated using the same formula, but substituting r_inner for r_outer:
V_inner = π * (r_inner)^2 * h
To find the volume of the metal, we subtract the volume of the inner cylinder from the volume of the outer cylinder:
V_metal = V_outer - V_inner
Given that the internal radius (r_inner) is 10cm and the thickness of the pipe (3cm), we can calculate the external radius (r_outer) by adding the thickness to the internal radius:
r_outer = r_inner + thickness
= 10cm + 3cm
= 13cm
Now we can calculate the volume of the metal:
V_metal = π * (r_outer)^2 * h - π * (r_inner)^2 * h
= π * (13cm)^2 * h - π * (10cm)^2 * h
= π * (169cm^2 - 100cm^2) * h
= π * 69cm^2 * h
Therefore, the volume of the metal used in making the 3cm thick pipe is π * 69cm^2 * h, where h is the height of the pipe.
To find the volume of the metal used in making the 3cm thick pipe, we need to subtract the volume of the inner cylinder (hollow part) from the volume of the outer cylinder.
First, let's calculate the volume of the internal cylinder using its radius:
Volume of internal cylinder = π * r^2 * h,
where r is the radius and h is the height (length) of the cylinder.
Given that the internal radius is 10cm and the thickness of the pipe is 3cm, the radius of the outer cylinder is the sum of the internal radius and the thickness:
Outer radius = internal radius + thickness = 10cm + 3cm = 13cm.
Next, let's calculate the volume of the external cylinder (including the hollow part):
Volume of external cylinder = π * R^2 * h,
where R is the outer radius.
Since we want to find the volume of the metal used in making the 3cm thick pipe, we need to find the difference between the volumes of the outer and inner cylinders:
Volume of metal used = Volume of external cylinder - Volume of internal cylinder.
Substituting the values:
Volume of metal used = π * R^2 * h - π * r^2 * h,
where h is the height of the pipe.
Note that the height (length) of the pipe does not affect the volume of the metal used, so we can ignore it in our calculations.
Now, let's calculate the volume of the metal used in making the 3cm thick pipe:
Volume of metal used = π * (R^2 - r^2),
where R is the outer radius (13cm) and r is the inner radius (10cm).
Substituting the values:
Volume of metal used = π * (13^2 - 10^2).
Calculating further:
Volume of metal used = π * (169 - 100).
Volume of metal used = π * 69.
Therefore, the volume of the metal used in making the 3cm thick pipe is approximately 216.67 cubic centimeters (rounded to two decimal places).