Opening Activity 10 in 2 in 4 in Find the volume of the rectangular pyramid.

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Presentation transcript:

Opening Activity 10 in 2 in 4 in Find the volume of the rectangular pyramid.

Opening Activity 1. A toy company makes rectangular sandboxes that measure 6 feet by 5 feet by 1.2 feet. A customer buys a sandbox and 40 cubic feet of sand. Did the customer buy too much or too little sand? Justify your answer. V=lwh V=(6)(5)(1.2) The sandbox has a volume of 36 cubic feet. 40 > 36 So too much sand was bought.

Chapter 8 Lesson 5 Volume of Pyramids

Objective: Students will find the volumes of pyramids.

The volume V of a pyramid is one third the area of the base B times the height of the pyramid h. In a polyhedron, any face that is not a base is called a lateral face. The lateral faces of a pyramid meet at a common vertex. The height of a pyramid is the distance from the vertex perpendicular to the base. Square/Rectangular Pyramid: Triangular Pyramid: h B h B

Example 1: Find the volume of a pyramid that has a height of 9 centimeters and a rectangular base with a length of 7 centimeters and a width of 3 centimeters. Draw a picture: h=9cm 7cm 3cm

Example 2: Find the volume of the pyramid. Round to the nearest tenth. 11m 8.1m h=6.4m

You can also use the formula for the value of a pyramid to find a missing height. Example 3: A rectangular pyramid has a volume of 525 cubic feet. It has a base of 25 feet by 18 feet. Find the height of the pyramid. Volume of a rectangular pyramid Fill in the dimensions given. Combine like terms. Divide both sides by 150.

Example 4: A triangular pyramid has a volume of 840 cubic inches. It has a base of 20 inches and a height of 21 inches. Find the height of the pyramid. Volume of a triangular pyramid Fill in the dimensions given. Combine like terms. Divide both sides by 70

Example 5: A scale model of an Egyptian Pyramid is shown. Find the volume of the square pyramid. 8 in 9 in Volume formula for a rectangular pyramid Fill in the dimensions given.