Transcript Volume & Surface Area - Arizona State University

Volume & Surface Area
Section 6.2
Volume
• The volume is a measure of the space
inside a solid object.
• Volume is measure of 3 dimensions.
• The units of volume are cube length or
length3.
• Example of volume units are cm3, cubic
feet, cubic meters or inches3.
Surface Area
• Surface area is the flat area on the
surface of a three-dimensional object.
• What you do is compute the area of all the
sides of an object and then add them up.
The Cube
• For an arbitrary cube with edges that have
length L, H, and W. The volume is
V = LWH.
• The surface area of the cube is the sum of
the areas of each face.
SA = 2LW + 2HW + 2LH.
H
W
L
The Sphere
• The volume of a sphere with radius r, is
V = (4/3)πr3.
• The surface area is SA = 4πr2.
The cylinder
• The volume of the cylinder is height of the cylinder times the area of
a circle. V = πr2h.
• The surface area of a cylinder has two parts. The ends are circles so
each circle has an area of πr2. The lateral surface can be thought of
as a rectangle wound into a circle. One side of the rectangle is h, the
other side is the circumference of the circle which is 2πr.
2πr
h
h
The pyramid and cone
• The pyramid and cone have similar formulas for
their volume. The basic volume formula is V =
(1/3)Ah. Where A is the area of the base.
• For a pyramid, the area of the base A is just the
area of a rectangle.
• For a cone, the area of the base is the area of a
circle.
pyramid
cone