Solid Figures: Volume and Solid Figures: Volume and Surface AreaSurface Area

Let’s review some basic solid Let’s review some basic solid figures…figures…

SphereSphere

A sphere is a ball. It has no faces, edges,

or vertices.

CubeCube

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 PrismRectangular 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.

CylinderCylinder

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 VolumeFinding Volume

We’re going to talk about how to find the volume of rectangular prisms and cylinders.

Volume: Rectangular PrismsVolume: 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 PrismsVolume: 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 = 9 x 6 x 5V = 270 cubic inches

Volume: CylindersVolume: Cylinders

The formula for finding the volume of a cylinder is pi x radius squared x height.

Volume: CylindersVolume: 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 12V = 2,411.52 cubic centimeters

Finding Surface AreaFinding Surface Area

Now we’re going to talk about how to find the surface area of rectangular prisms and cylinders.

Surface Area: Rectangular Surface Area: Rectangular PrismsPrisms

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 Surface Area: Rectangular PrismsPrisms

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: CylindersSurface 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: CylindersSurface 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 + 75.36SA = 100.48 square feet

Remember…Remember…

Since multiplication is commutative, it doesn’t matter what order you multiply your numbers in when you find volume.