UNIT 4. SOLIDS / 3-D SHAPES /
POLYHEDRONS
1. DEFINITION
• A solid is a three dimensional shape.
2. TYPES OF SOLIDS AND AREAS
SOLIDS. DEFINITIONS
AND PROPERTIES
DRAWING SOLIDS
CUBE
• The most simple solid.
• It's got all its sides
congruent.
NETS FOR SOLIDS
AREAS
TOTAL AREA =
= 6 X Square area =
SOLIDS. DEFINITION
AND PROPERTIES
DRAWING SOLIDS
CUBOID
• Its six faces are
quadrilaterals.
• The most common cuboid
is a right rectangular
cuboid.
• Its faces are rectangles
forming right angles.
NETS FOR SOLIDS
AREAS
LATERAL AREA
=
= Perimeter of the base x height =
TOTAL AREA =
Lateral area + 2 x area of the base=
SOLIDS. DEFINITION
AND PROPERTIES
DRAWING SOLIDS
PRISM:
• A solid with two
congruent polygonal bases
and all its faces are
parallelograms.
• The most common is the
right rectangular prism.
Its faces are rectangles
that form right angles
with the bases.
• Types:
-Triangular prism.
-Rectangular prism (cuboid)
-Pentagonal prism.
-Hexagonal prism
NETS FOR SOLIDS
AREAS
LATERAL AREA =
= Perimeter of the base x height =
TOTAL AREA =
=Lateral area + 2 x area of the base
SOLIDS. DEFINITION
AND PROPERTIES
DRAWING SOLIDS
PYRAMID:
• A solid with a polygonal base
and triangular faces that
meet at the vertex on the
top.
• The most common pyramid has
an square in its base.
NETS FOR SOLIDS
AREAS
LATERAL AREA =
= n x area of the tringular face =
TOTAL AREA =
= Lateral area + Area of the base =
SOLIDS. DEFINITION
AND PROPERTIES
DRAWING SOLIDS
CYLINDER:
• It's a prism with two
congruents circular bases.
NETS FOR SOLIDS
AREAS
LATERAL AREA =
= Length of the circumference x Height=
TOTAL AREA =
= Lateral area + 2 x Area of the circle =
=
SOLIDS. DEFINITION
DRAWING SOLIDS
AND PROPERTIES
CONE:
1. It's a pyramid with circular
base.
NETS FOR SOLIDS
AREAS
LATERAL AREA=
=pxrxg
TOTAL AREA=
= LATERAL AREA + BASE AREA
SOLIDS. DEFINITION AND
PROPERTIES
DRAWING SOLIDS
SPHERE:
•
It's a perfectly round solid.
3. VOLUME OF 3-D SHAPES:
PRISM
VOLUME = Area of the base x Height =
V = Bxh
Exploring:
1. Find the total area and the volume of a right prism 15cm tall whose
bases are rhombus with diagonal of 8cm and 6cm.
2. Find the total area and the volume of a right prism 6dm tall whose
bases are pentagons with side of 2.5dm.
CYLINDER
VOLUME = Area of the base
x Height
V = B x h
Exploring:
1. Find the lateral and total areas and the volume of a cylinder 4cm tall
and a circle at the base of r=1.5cm
PYRAMID
Volume= 1/3 of base x height=
1/3 x(B x h)
Exploring:
1. Calculate the volume of a regular quadrangular pyramid with base
side length: 10cm and its height: 12cm.
CONE
Volume= 1/3 of base x height=
=1/3 x (B x h)
Exploring:
1. Calculate the volume of a cone with a height of 15cm and a
generatrix of 17cm.