An Artisan has 63 kg of metal of density 7,000kg/m3. He intends to use make a rectangular pipe with external dimensions 12 cm by 15 cm and internal dimensions 10 cm by 12 cm. Calculate the length of the pipe in meters.
To solve this problem, we need to follow these steps:
Step 1: Calculate the volume of the rectangular pipe.
Step 2: Convert the mass of the metal from kilograms to cubic meters using its density.
Step 3: Use the formula for density to calculate the length of the pipe.
Let's start with step 1:
Step 1: Calculate the volume of the rectangular pipe.
The volume of a rectangular pipe can be calculated by subtracting the volume of the inner dimensions from the volume of the outer dimensions.
Volume of outer dimensions = Length × Width × Height
= 0.12 m × 0.15 m × h, where h is the height in meters.
Volume of inner dimensions = Length × Width × Height
= 0.10 m × 0.12 m × h, where h is the height in meters.
The volume of the rectangular pipe is the difference between the volume of the outer dimensions and the volume of the inner dimensions:
Volume of the rectangular pipe = (0.12 m × 0.15 m × h) - (0.10 m × 0.12 m × h)
Step 2: Convert the mass of the metal from kilograms to cubic meters using its density.
The density of the metal is given as 7,000 kg/m^3. Since the mass is given as 63 kg, we can use the formula:
Mass = Density × Volume
Solve the formula for Volume:
Volume = Mass / Density
= 63 kg / 7,000 kg/m^3
= 0.009 m^3
Step 3: Use the formula for density to calculate the length of the pipe.
Now, we can equate the volume of the rectangular pipe calculated in step 1 with the volume calculated in step 2.
Volume of the rectangular pipe = 0.009 m^3
(0.12 m × 0.15 m × h) - (0.10 m × 0.12 m × h) = 0.009 m^3
To calculate the value of h, we can simplify the equation:
(0.018 m^2 × h) - (0.012 m^2 × h) = 0.009 m^3
0.006 m^2 × h = 0.009 m^3
h = (0.009 m^3) / (0.006 m^2)
h = 1.5 m
Therefore, the length of the pipe is 1.5 meters.