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 = 9 x 6 x 5 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, 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 = 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 = SA = square feet

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