Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 58
Chapter 12. Surface Area & Volume
Cuboids, Rectangular Prisms and Cubes
Cubes and Cuboids
The volume of a cuboid is simply:
Which can be written as:
Volume = width × depth × height
V = wdh
Example Calculation
Find the volume and surface area of this
cuboid.
V = 4×5×10 = 200
Volume of a prism
A prism has the same cross section all along its length!
A cross section is the shape you get when cutting straight across an object
The cross section of this object is a triangle ...
.. it has the same cross section all along its length ...
... and so it's a triangular prism.
No Curves!
12. Surface Area & Volume
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
A prism is officially a polyhedron, which means all sides should be flat. No curved sides.
So the cross section will be a polygon (a straight-edged figure). For example, if the cross
section was a circle then it would be a cylinder, not a prism.
These are all Prisms:
Square Prism:
Cross-Section:
Section:
(yes, a cube is a
all along its length)
Triangular Prism:
prism,
Cross-Section:
Cube:
because
Pentagonal Prism:
Cross-
it
is
a
square
Cross-Section:
Regular and Irregular Prisms
All the previous examples are Regular Prisms, because the cross section is regular (in
other words it is a shape with equal edge lengths)
Here is an example of an Irregular Prism:
Irregular Pentagonal Prism: Cross-Section:
(It is "irregular" because the
Pentagon is not "regular"in shape)
12. Surface Area & Volume
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Volume of a Prism
The Volume of a prism is simply the area of one end times the length of the prism
Volume = Area × Length
Example: What is the volume of a prism
whose ends are 25 in2 and which is 12 in
long:
Answer: Volume = 25 in2 × 12 in = 300 in3
Volume of a Cylinder
A cylinder can be thought of as a circular prism so its volume can be found using
Volume
= area of cross-section  length
= area of circular end  length
From this we can find a formula for the volume.
We usually think of a cylinder as standing upright so that its length is represented by h (for
height).
r
If the radius of the end circle is r, then the area of the
cross-section is r2
Therefore
12. Surface Area & Volume
volume = r2  h
= r2 h
h
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Exercise 1
1.
Find the volume of each of the following prisms.
2 cm
a)
b)
3 cm
2 cm
8 cm
7 cm
18 cm
10 cm
5 cm
c)
d)
15 cm
12 cm
8 cm
18 cm
8 cm
11 cm
12 cm
e)
f)
2 cm
2 cm
8 cm
15 cm
10 cm
8 cm
9 cm
12 cm
Depth of 12 cm
Depth of 20 cm
2)
Find the volume of the following solids. Take = 3.142 and give your answers
correct to 3 s.f. Draw diagrams of the cross-sections
first.
a)
A tube of length 20 cm. The inner radius is 3 cm
and the outer radius is 5 cm.
12. Surface Area & Volume
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
b)
A solid of length 6.2 cm, whose cross-section consists of a square of side 2 cm
surmounted by a semicircle.
c)
A solid made of two half-cylinders each of length 1 cm. The radius of the larger one is
10 cm and the radius of the smaller one is 5 cm.
3)
Find the volume of the following solids which have a length as given and a uniform
cross-section as shown in the diagram.
a) Length = 15cm
b) length = 5cm
4.6 cm
c) length = 10.5cm
4.6 cm
7 cm
7.8 cm
6.5 cm
8.6 cm
15 cm
4)
A greenhouse is 10 m long and has a cross-section which is a square of side 5 m on
top of which is a triangle, as shown in the diagram.
The overall height of the greenhouse is 7.5 m.
Calculate the volume of air inside the greenhouse.
7.5 m
12. Surface Area & Volume
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