TOPIC 3: THREE DIMENSIONAL FIGURES ~ MATHEMATICS FORM 4
Three Dimensional Figures
drinking water tank?
What about the amount of cloth for the pocket covers of your radio, curtain, suit, gown, trousers, set of table clothes, etc.
drawing a three dimensional object it is important to show that it is
not a drawing of a flat object. Are usually drawn on a two dimensional
plane by making oblique drawings under certain rules as follows:
- Paralled lines are drawn parallel.
- Vertical lines are drawn up and down the page.
- Hidden edges are drawn dotted.
- Construction lines to guide the eyes are drawn thinly.
are several ways of doing the drawing that corresponds to looking at
the cube from different angles. The figure shows two ways of doing it.
dimensional shapes have many attributes such as faces, edges
andvertices. The flat surfaces of the 3D shapes are called the faces.
The line segment where two faces meet is called an edge. Avertexis a
point where 3 edges meet.
finding the angle between the line and a plane in a three dimensional
geometry, we use the right angled triangle. Joining the line to define
the angle between the line and the plane that provides the least
possible angle. Also, projection of one line to another on the plane is
the projection of VA on ABCD is AX. AC= square root of (AB2 +BC2)
=square of 42+42 =square root of 32. AX =1/2square root of32. cos
(1/2square root 32)/5=0.5657, so VAX is 55.6.
are infinite possible lines that could be drawn on planes, making
different angles with each other. The angle between planes is the angle
between lines within those planes, Must be the lines which are at the
middle of the plane for non rectangular planes and any other lines for
rectangular planes. Then Right angled triangles are used to find the
angles between those planes.
you want to know the amount of the covering the surface of a blue band
margarine can, then you are finding the surface area of a right
cylinder. Total surface area of the can is the sum of the areas of the
top and bottom. Circular surfaces plus the area of the curved surface,
the cylinder is opened up, the curved surface flattens out to form a
rectangle. The length of the rectangle is 2Πr(the circumference of the
circular base) and the width is h (the height of the cylinder).
right rectangular pyramid is such that the rectangle is 12cm by 8cm and
each slant edge is 12cm. Find the total surface area of the pyramid.
altitude of a rectangular prism is 4cm and the width and lengths of its
base are 2cm and 3cm respectively calculate the total surface area of
The following diagram shows a cylinder of diameter 20 units and height 9
units. What is its curved surface area?
Volume of Three Dimensional Objects
the volume of a pyramid is one – third the product of its altitude
(height) and its base area.
figure above shows a sphere of radius r, if the sphere can be put
inside a cylinder of the same radius” r”, then the height h = 2r.
pipe made of metal 1cm thick, has an external (outside) radius of 6cm.
Find the volume of metal used in making 4m of pipe. Use π=3.14
What is the volume of a right prism whose base is a regular hexagon ( n
= 6) with a side of the base 4cm long and the height of the prism.
A cylinder and sphere have the same volume. If the radius of the sphere
is 5cm and radius of the cylinder is 3cm, Calculate height of the
diagram shows a barn. What is the volume of the barn? (The length of
the hypotenuse in the right triangle is rounded to the nearest foot.)
You can now have a summary of the important formulas for calculating volume of some three dimensional figures as follows:-