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Solid Figures: Volume and Surface Area

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Solid Figures: Volume and Surface Area

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

- A cubeis like a box.
- It has six faces, six edges, and four vertices.
- All of a cube’s faces and edges are equal.

- 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.

- 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.”

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

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

- 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

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

- 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

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

- The formula for finding the surface area of a rectangular prism is 2(length x width) + 2(length x height) + 2(width x height).

- 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

- 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)

- 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

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