SOLID GEOMETRY
DONE BY: ABDELAZIZ HUSAIN ALI
GRADE: 12-02
WHAT IS SOLID GEOMETRY?
• In mathematics, solid geometry was the traditional name for
the geometry of three-dimensional Euclidean space — for
practical purposes the kind of space we live in. Geometry
deals with the measurements of volumes of various solid
figures including cylinder, circular cone, truncated cone,
sphere, and prisms.
ABOUT SOLID GEOMETRY
HEIGHT
• It is called three-dimensional, or 3D because there are three
dimensions: width, depth and height.
WIDTH
SIMPLE SHAPES
• Some of the simplest shapes:
PROPERTIES OF SOLID GEOMETRY
• Volume (think of how much water it could hold).
• Surface area (think of the area you would have
to paint).
• How many vertices (corner points), faces and
edges they have.
SAT QUESTIONS ABOUT
SOLID GEOMETRY
1) A cubic box has sides of length x. Another
cubic box has sides of length 4x. How many of
the boxes with length x could fit in one of the
larger boxes with side length 4x?
A.
B.
C.
D.
E.
80
64
40
16
4
EXPLANATION
• The volume of a cubic box is given by (side
length) 3. Thus, the volume of the larger box is
4x3 = 64x3, while the volume of the smaller box is
x3. Divide the volume of the larger box by that of
the smaller box, 64x3 / x3=64.
2) I have a hollow cube with 3 inch per side
suspended inside a larger cube of 9 inch per
side. If I fill the larger cube with water and the
hollow cube remains empty yet suspended
inside, what volume of water was used to fill
the larger cube?
A.
B.
C.
D.
E.
73in3
72in3
702in3
912in3
698in3
EXPLANATION
• Determine the volume of both cubes and
then subtract the smaller from the larger.
The large cube volume is 9×9×9=729in3
and the small cube is3×3×3=27in3.
The difference is 702 in3.
3) If the volume of a cube is 50ft3, what
is the volume when the sides double in
length?
A.
B.
C.
D.
E.
500ft3
200ft3
300ft3
400ft3
600ft3
EXPLANATION
• Using S as the side length in the original cube, the original is
S×S×S. Doubling one side and tripling the other gives
2S×2S×2S for a new volume formula for 8S×S×S, showing that
the new volume is 8× greater than the original.
4) A spherical orange fits snugly inside a small
cubical box such that each of the six walls of
the box just barely touches the surface of the
orange. If the volume of the box is 64in3, what
is the surface area of the orange in square
inches?
A.
B.
C.
D.
E.
64π in2
256π in2
128π in2
32π in2
16π in2
EXPLANATION
The volume of a cube is found by V= s3.
Since V = 64, s = 4.
The side of the cube is the same as the diameter of the sphere.
Since d = 4, r = 2.
The surface area of a sphere is found by
SA = 4πr2 = 4π22= 16π in2.
5) A cylinder has a volume of 20 in3. If the
radius doubles, what is the new volume?
A.
B.
C.
D.
E.
80 in3
40 in3
100 in3
60 in3
50 in3
EXPLANATION
• The equation for the volume of the cylinder is πr2h. When the
radius doubles (r becomes 2r)
• You get π(2r)2h = 4πr2h. So when the radius doubles, the
volume quadruples, giving a new volume of 80 in3.
HERE IS A WEBSITE WHERE YOU CAN
PRACTICE MORE ABOUT SOLID
GEOMETRY
• http://www.khanacademy.org/math/geometry/basicgeometry/volume_tutorial/e/solid_geometry
HERE IS VIDEO DONE BY ME
HERE IS ANOTHER VIDEO
HERE IS OUR GROUP WEBSITE
http://geometry1202.weebly.com/
HOPE YOU LIKE IT 