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Solid Figures: Volume and Surface Area

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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  1. Solid Figures: Volume and Surface Area

  2. Let’s review some basic solid figures…

  3. Sphere • A sphere is a ball. • It has no faces, edges, or vertices.

  4. 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.

  5. 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.

  6. 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.”

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

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

  9. 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

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

  11. 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

  12. Finding Surface Area • Now we’re going to talk about how to find the surface area of rectangular prisms and cylinders.

  13. 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).

  14. 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

  15. 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)

  16. 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

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

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