SOLUTION: An iron pipe 3 meters long has an internal diameter of 30 cm. The iron is 12 mm thick. Find the lateral area and volume of iron in the pipe. in Meters

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Question 1198094: An iron pipe 3 meters long has an internal diameter of 30 cm. The iron is 12 mm thick. Find the lateral area and volume of iron in the pipe. in Meters
Found 2 solutions by Alan3354, math_tutor2020:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An iron pipe 3 meters long has an internal diameter of 30 cm. The iron is 12 mm thick. Find the lateral area and volume of iron in the pipe. in Meters
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Not in meters.
Area in square meters.
Vol in cubic meters.
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Internal radius r1 = 15 cm
External radius r2 = 15 + 1.2 = 16.2 cm
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Lateral area (outside surface) = pi*16.2^2 sq cms
Not clear if the ends are to be included, or the inside surface.
1 sq meter = 10,000 sq cms
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Cross-sectional area = pi*16.2^2 - pi*15^2 sq cms
= pi*(262.44 - 225) = 37.44pi sq cms
Vol = 37.44pi*300 cubic cms
1 cubic meter = 1,000,000 cc

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Place the pipe to be vertical, so the length of 3 meters can be interpreted as the height of the cylinders.
h = 3 = height

The internal diameter is 30 cm
d = 30
which cuts in half to get the radius
r = d/2 = 30/2 = 15
This is the radius of the internal cylinder.

12 mm = 12/10 = 1.2 cm
15+1.2 = 16.2 cm is the radius of the larger outer cylinder

LSA = lateral surface area of the larger cylinder
LSA = 2*pi*16.2*3
LSA = 97.2pi
Replace pi with 3.14 or something similar to that effect to compute the approximate LSA value.
The units are in square cm, and it represents how much area to paint over the outer cylinder.

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Volume:

The inner cylinder has a radius of r = 15
V = pi*r^2*h
V = pi*15^2*3
V = pi*675
V = 675pi

The outer cylinder has a radius of r = 16.2
V = pi*r^2*h
V = pi*(16.2)^2*3
V = pi*787.32
V = 787.32pi

Subtract the volumes to determine the amount of space taken up by the iron cylindrical shell. In other words, we're excluding the empty space taken up by the inner cylinder.
V = (outer cylinder volume) - (inner cylinder volume)
V = 787.32pi - 675pi
V = (787.32 - 675)pi
V = 112.32pi
Like before, replace pi with 3.14 (or more decimal digits) to find the approximate volume.

This is a slight alternative formula
V = (R^2-r^2)pi*h
where
R = radius of larger or outer cylinder
r = radius of smaller or inner cylinder
h = height