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.
so he has 63/7000 m^3
and 1 m^3 is 100^3 cm^3
so he has 63/7000 * 1000000 cm^3
or 9000 cm^3 available
let the length be h
area of cross-section
= 12(15) - (10)(12) = 60 cm^2
60h = 9000
h = 150 cm long or 1.5 m
To calculate the length of the pipe, we first need to determine its volume. The external dimensions of the pipe are given as 12 cm by 15 cm, and the internal dimensions are given as 10 cm by 12 cm.
To find the volume of the pipe, we need to calculate the volume of the outer rectangular solid and subtract the volume of the inner rectangular solid.
Volume of the outer rectangular solid:
Length = 15 cm = 0.15 m
Width = 12 cm = 0.12 m
Height = unknown (let's call it h)
Volume = Length * Width * Height = 0.15 m * 0.12 m * h = 0.018h m^3
Volume of the inner rectangular solid:
Length = 12 cm = 0.12 m
Width = 10 cm = 0.10 m
Height = unknown (let's call it h)
Volume = Length * Width * Height = 0.12 m * 0.10 m * h = 0.012h m^3
Therefore, the volume of the pipe is:
0.018h m^3 - 0.012h m^3 = 0.006h m^3
Now, let's find the mass of the metal used in the pipe. We know that the density of the metal is 7,000 kg/m^3, and the volume of the pipe is 0.006h m^3.
Mass = Density * Volume = 7,000 kg/m^3 * 0.006h m^3
Since we know that the Artisan has 63 kg of metal, we can set up an equation:
7,000 kg/m^3 * 0.006h m^3 = 63 kg
Simplifying this equation, we get:
0.042h = 63
Multiplying both sides by 1/0.042 to isolate h, we get:
h = 63 / 0.042
h ≈ 1500
Therefore, the height of the pipe is approximately 1500 meters.
To find the length of the pipe, we can use the external dimensions:
Length = 15 cm = 0.15 m
Therefore, the length of the pipe is 0.15 meters.