Transcript The Volume of a Geometric Solid

The Volume of a
Geometric Solid
By Tyrissa Schroeder
Pages: 529-537
Volume of Rectangular and Cubes
Prisms

Volume- is the number of cubic units required to fill a 3demenisional figure.

Rectangular Solid- is a solid in which all six faces are rectangles.
V=lwh, Length(width)(height)
HH
V= 7(4)(14)=392ft cubed
L
W

Cube- a solid when all six faces are squares.
V= S^3
5
5
5
V= 5^3
V= 5(5)(5)=125inches cubed
More Geometric Solids

Cylinder- is a solid in which the
bases are the circles and are
perpendicular to the height.
4in
V= pie(r^2)(height)
8in

V= 3.14(2^2)(8)=100.48in
Sphere- is a three dimensional
figure made up of all points a
given distance from the center.
6cm.
V= 4/3(pie)(r^3)
V=4/3(3.14)(6^3)= 150.72cm
Composite Solids
 To find the volume of a solid
with a missing center such as
a cube with a cylinder deleted
from the center, you will find
the volume of the cube then
subtract the volume of the
cube.
5m
Example:
20m
V= S^3 – Pie(r^2)(20)
V= 20^3 – 3.14(5^2)(20)=
V= 8,000m – 1,570m=
6,430m^3
20m
20m
Word Problem

A delivery truck is 3.5 meter long and 2.5 meter
wide and 2 meter high.( not including the cab)
Has a large box that is 1.5 meters long, 1.4
meters wide and 1.1 meters tall. What is the
Volume of the space remaining in the truck?
 Solution: Find the Volume of the truck then find
the volume of the box and subtract.
Truck Volume= lwh, 3.5(2.5)(2)= 17.5
Box Volume = lwh, 1.5(1.4)(1.1)= 2.31
17.5 – 2.31= 15.19 meters^3
More Practice on Geometric Solids

Rectangular Solid-
10 ft
V= lwh
V= 10(8)(5)= 140ft^3
5 ft
8 ft

CubeV= S^3
27 cm
V= 27^3, 27(27)(27)= 729
cm^3
27 cm
27 cm
Cylinder and Sphere

Cylinder- What is the
volume difference?
Volume= Pie(r^2)(h)
Yellow Tube= 6 in tall,
radius of 1in.
V= 3.14(1.5)^2(6)=
42.39in^2
Green Tube= 8.5 in tall,
radius of 3in.
V= 3.14(3)^2(8)=226.08in^2
V= 226.08 - 42.39in=
183.69
V= 184in^3
Sphere2 in
V= 4/3(pie)(r^3)=
V=4/3(3.14)(2^3)= 33.49 in^3
Formulas
Rectangular Solid
V=lwh
V= 7(4)(14)= 392 ft^3
Cube
V= S^3
V= 5(5)(5)= 125 in ^3
Cylinder
Sphere
Composite Solids
V= Pie(radius^2)(h)
V=3.14(4^2)(10)= 502.4ft ^2
V= 4/3(pie)(radius^3)
V= 4/3(3.14)(3^3)= 113
mm^3
V= S^3 – pie(radius^2)(h)
V= 17^3 – 3.14(3^2)(15)=
67.4inches^3
Thank you!!