 # Pyramids Surface Area and Volume. Suppose we created a rectangular pyramid from a rectangular prism. Suppose we conducted an experience similar to yesterday’s.

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Pyramids Surface Area and Volume

Suppose we created a rectangular pyramid from a rectangular prism. Suppose we conducted an experience similar to yesterday’s lesson where we fill the rectangular prism with the contents of the rectangular prism.

What do you think is the relationship between the volume of the prism and the volume of the pyramid?

How are finding the volumes of the cones and rectangular prisms alike?

Suppose the rectangular prism is a cube with side lengths of 4 inches. 4 inches Find the volume of the prism and the pyramid. Volume of the Rectangular Prism = 64 inches cubed. Volume of the Rectangular Pyramid = 21.33 inches cubed.

The vertex of the pyramid is in the center of the top face in the rectangular prism. 4 inches How can we use the Pythagorean Theorem to find the height of the triangular face of the rectangular pyramid? Find this length.

Find the surface area of the pyramid. 4 inches 4.47 inches Total Surface Area of the Pyramid = 51.76 inches squared. Surface Area of one Triangular Face = 8.94 inches squared. 4 Triangular Faces = 35.76 inches squared Surface Area of the Base = 16 inches squared.

Practice Complete Question 16 and 17 on page 56.

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