# Homework Help: Calculate volume and surface area of a boiler

1. Jan 29, 2012

### scientist

1. The problem statement, all variables and given/known data
A boiler drum is equipped with hemispherical heads (i.e. the two heads together make a sphere.) The diameter of the drum is 0.8 meters and the drum is 5 meters in length.

Calculate: a.) The area of insulation required to cover the entire drum.
b.) The total volume of the drum.

2. Relevant equations
Cylinder total surface area = (2)(pi)(r)(h) + (2)(pi)(r2)
Sphere total surface area = (4)(pi)(r2)
Cylinder volume = (pi)(r2)(L)

3. The attempt at a solution

a) i) Cylinder total surface area = (2)(pi)(r2)(h) + (2)(pi)(r2 )
= (2) (3.14) (0.4)(5m) + (2)(3.14) (0.4)2
= 12.56 m2 + 1
= 13.56 m2 insulation required to cover the drum.

ii) Sphere total surface area = (4)(pi)(r2)
= (4) (3.14) (0.4)2
= 2 m2 insulation required to cover the two heads.

iii) Total surface area i+ ii = 13.56 m2 + 2 m2
= 15.56 m2 total insulation required to cover the entire drum.

b) Cylinder volume = (pi)(r2)(L)
= (3.14)(0.42)(5m)
= 2.5 m2 total volume of the drum.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Jan 29, 2012

### Delphi51

Drop the second term! There are no ends on the cylinder; they have been replaced by the hemispheres. And where did the r2 come from? Just r. By the way, you can easily copy symbols like the square ² from my signature or here:
https://www.physicsforums.com/blog.php?b=346 [Broken]

total surface area = (2)(pi)(r)(h) + (4)(pi)(r² )

Last edited by a moderator: May 5, 2017