A cylindrical pipe made, is 3cm thick if the lntemal radius of the pipe is 10cm, find the volume of the metal used in making 3m of the pipe
the bot is wrong again
Volume of metal = π × (13² - 10²) × 300 cm^3
= π (69)(300) cm^3
= appr 65,031 cm^3
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math questions. Poor students!!
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To find the volume of the metal used in making the pipe, we need to find the difference between the volumes of the outer and inner cylinders.
First, let's find the volume of the outer cylinder.
The external radius of the pipe (including the thickness) is the sum of the internal radius and the thickness. Therefore, the external radius is 10cm + 3cm = 13cm.
The height of the pipe is given as 3m, which is equivalent to 300cm.
The volume of the outer cylinder is given by the formula: V_outer = π * r_outer^2 * h = π * 13^2 * 300 = 507,960 cm³.
Next, let's find the volume of the inner cylinder.
The volume of the inner cylinder is given by the formula: V_inner = π * r_inner^2 * h = π * 10^2 * 300 = 94,248 cm³.
Finally, the volume of the metal used in making the pipe is the difference between the volumes of the outer and inner cylinders:
V_metal = V_outer - V_inner = 507,960 cm³ - 94,248 cm³ = 413,712 cm³.
Therefore, the volume of the metal used in making 3m of the pipe is 413,712 cm³.
To find the volume of the metal used in making 3m of the pipe, we need to break down the calculation into two parts: the volume of the outer cylinder and the volume of the inner cylinder.
First, let's find the volume of the outer cylinder.
The external radius of the pipe is the sum of the internal radius and the thickness, which is 10cm + 3cm = 13cm.
The height of the outer cylinder is given as 3m, which is equal to 300cm.
The formula for the volume of a cylinder is given by 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(13cm)^2 * 300cm.
Next, let's find the volume of the inner cylinder.
The radius of the inner cylinder is given as 10cm, and its height is also 3m, or 300cm.
Therefore, the volume of the inner cylinder is V_inner = π(10cm)^2 * 300cm.
Now, to find the volume of the metal used, we subtract the volume of the inner cylinder from the volume of the outer cylinder:
V_metal = V_outer - V_inner.
Substituting the values into the equation, we have:
V_metal = π(13cm)^2 * 300cm - π(10cm)^2 * 300cm.
Simplifying the equation:
V_metal = π * 169cm^2 * 300cm - π * 100cm^2 * 300cm.
Finally, calculating the value:
V_metal = π * 50700cm^3 - π * 30000cm^3.
We can further simplify this by factoring out π:
V_metal = π (50700cm^3 - 30000cm^3).
V_metal = π * 20700cm^3.
Hence, the volume of the metal used in making 3m of the pipe is 20700π cm^3.
We can start by finding the external radius of the pipe, which would be the sum of the internal radius and the thickness:
External radius = 10cm + 3cm = 13cm
Now we can find the volume of the metal used in making 1m of the pipe:
Volume of metal = π × (external radius² - internal radius²) × height
Volume of metal = π × (13² - 10²) × 100cm
Volume of metal = 1,170π cm³
To find the volume of the metal used in making 3m of the pipe, we simply multiply the above value by 3:
Total volume of metal = 1,170π cm³ × 3
Total volume of metal = 3,510π cm³
Therefore, the volume of metal used in making 3m of the pipe is 3,510π cm³.