A cylindrical pipe 28m long. Its internal radius is 3.5cm and external radius is 5cm. Calculate the volume in cm of metal used in making the pipe (2) the volume of water in metres that the pipe can hold.
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Answer
A cylinder pipe is 28m long. It's internal radius is 3.5cm and external radius is 5cm. Calculate the volume in cm3
since the area of a circle is πr^2, the volume of metal is
2800π(5^2 - 3.5^2) = 112,154 cm^3
the water volume (inside only) is 28π*0.035^2 = 0.11 m^3
(2) internal volume = π * 3.5^2 * 2800 ... cm^3
external volume = π * 5^2 * 2800 ... cm^3
the difference in the volumes is the volume of metal in the pipe ... cm^3
volumes are measured in cubic units ... 1E6 cm^3 = 1 m^3
112.200cmcube
To calculate the volume of metal used in making the pipe, we need to find the difference between the volume of the outer cylinder and the inner cylinder.
1) Volume of the outer cylinder:
The formula to calculate the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
In this case, the outer radius is 5 cm and the height is 28 m.
First, let's convert the height from meters to centimeters:
Height (h) = 28 m = 28 x 100 cm = 2800 cm
Now, we can calculate the volume of the outer cylinder:
V_outer = π(5 cm)^2 × 2800 cm
2) Volume of the inner cylinder:
Using the same formula, the volume of the inner cylinder can be calculated.
In this case, the inner radius is 3.5 cm and the height is still 2800 cm.
V_inner = π(3.5 cm)^2 × 2800 cm
3) Volume of metal used:
Now, we can find the difference between the volumes of the outer and inner cylinders to calculate the volume of metal used.
Volume of metal used = V_outer - V_inner
To calculate the volume of water the pipe can hold, we'll use the formula for the volume of a cylinder.
4) Volume of water:
The height of the pipe remains the same - 28 m.
Now, let's convert the external radius from centimeters to meters:
Outer radius (r) = 5 cm = 5/100 m = 0.05 m
V_water = π(0.05 m)^2 × 28 m
Therefore, the volume used in making the pipe is calculated in cm³, and the volume of water the pipe can hold is calculated in m³.