Solid figures volume and surface area
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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.

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Solid Figures: Volume and Surface Area

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Solid figures volume and surface area

Solid Figures: Volume and Surface Area


Let s review some basic solid figures

Let’s review some basic solid figures…


Sphere

Sphere

  • A sphere is a ball.

  • It has no faces, edges, or vertices.


Solid figures volume and surface area

Cube

  • A cubeis like a box.

  • It has six faces, six edges, and four vertices.

  • All of a cube’s faces and edges are equal.


Rectangular prism

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

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

Finding Volume

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


Volume rectangular prisms

Volume: Rectangular Prisms

  • The formula for finding the volume of a rectangular prism is volume = length xwidth xheight, or V = l x w xh.


Volume rectangular prisms1

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

Volume: Cylinders

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


Volume cylinders1

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

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

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 prisms1

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

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 cylinders1

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

Remember…

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


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