Solid Figures: Volume and
Surface Area
Let’s review some basic solid
figures…
Sphere

A sphere is a ball.
 It has no faces, edges,
or vertices.
Cube

A cube is like a box.
 It has six faces, six
edges, and four
vertices.
 All of a cube’s faces
and edges are equal.
Rectangular Prism

A rectangular prism is
also like a box.
 It has six faces, six
edges, and four
vertices.
 All of its faces are
either squares or
rectangles.
Cylinder

A cylinder is like a
soup can.
 It has two circular
faces on each end, but
no edges or vertices.
 You could say that a
cylinder is a “circular
prism.”
Finding Volume

We’re going to talk about how to find the
volume of rectangular prisms and cylinders.
Volume: Rectangular Prisms

The formula for finding the volume of a
rectangular prism is volume = length x
width x height, or V = l x w x h.
Volume: Rectangular Prisms

Suppose you have a rectangular prism that
is 9 inches long, 6 inches wide, and 5 inches
high.
 What is the volume of this rectangular
prism?
V=9x6x5
 V = 270 cubic inches
Volume: Cylinders

The formula for finding the volume of a
cylinder is pi x radius squared x height.
Volume: Cylinders

Suppose you have a cylinder with a height
of 8 centimeters and a radius of 12
centimeters.
 What is the volume of this cylinder?
 V = 3.14 x (8)^2 x 12
 V = 2,411.52 cubic centimeters
Finding Surface Area

Now we’re going to talk about how to find
the surface area of rectangular prisms and
cylinders.
Surface Area: Rectangular
Prisms

The formula for finding the surface area of a
rectangular prism is 2(length x width) +
2(length x height) + 2(width x height).
Surface Area: Rectangular
Prisms






Suppose you have a rectangular prism that is 7
meters long, 3 meters high, and 4 meters wide.
What is the surface area of this rectangular prism?
SA = 2(7 x 4) + 2(7 x 3) + 2(4 x 3)
SA = 2(28) + 2(21) + 2(12)
SA = 56 + 42 + 24
SA = 122 square meters
Surface Area: Cylinders

The formula for finding the surface area of a
cylinder is SA = (2 x pi x radius squared) +
(2 x pi x radius x height)
Surface Area: Cylinders

Suppose you have a cylinder with a height
of 6 feet and a radius of 2 feet.
 What is the surface area of this cylinder?
 SA = (2 x pi x 2^2) + (2 x pi x 2 x 6)
 SA = (2 x 3.14 x 4) + (2 x 3.14 x 12)
 SA = 25.12 + 75.36
 SA = 100.48 square feet
Remember…

Since multiplication is commutative, it
doesn’t matter what order you multiply your
numbers in when you find volume.