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7.5 What's The Volume With One Base? Pg. 14 Volume of a Pyramid and Cone

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7.5 – Whats the Volume With One Base? Volume of a Pyramid and Cone Today you will continue making connections between prisms and pyramids.

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7.24 – VOLUME OF A PYRAMID Sara thinks that she can compare the volume of a pyramid to the volume of a cube. a. What fraction of the cube with edge length 6 is the pyramid. Discuss this with your team and make an estimate.

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b. Use computer software to compare the volume of a prism versus a pyramid. Then come up with a formula for the volume of a pyramid. video V = BH 1313

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7.25 – PRACTICE Now that you have seen that the volume of a pyramid is 1/3 the volume of a prism with the same base area, solve for the volume of the pyramid below. Be sure to use the correct height!

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V = BH 1313 V = 1313 (64) (3) V = 64 un 3

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V = BH 1313 V = 1313 (84) (19) V = 532 un 3

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V = BH 1313 B = ½bh B = ½(4)(2.8) B = 5.6x 5 triangles =28

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7.26 – CONES While finding the volumes of the pyramids above, Jamal asks, "But what if its a cone? How would you find its volume?" Note that a cone is a three- dimensional figure that consists of a circular face, called the base, a point called the apex, that is above the shape, and the lateral surface that connects the two.

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a. Discuss Jamal's question with your team. Then write a response explaining how to find the volume of a cone based on the formula for the volume of a pyramid. V = BH 1313

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b. Find the volume of the cone. Show all work.

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V = r 2 H 1313 V = (4) 2 (7) 1313 V = 37.33 yd 3

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V = r 2 H 1313 V = (8) 2 (9.53) 1313 V = 203.31 cm 3 O A tan 40 = 8a8a a = 9.53

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7.27 – VOLUME OF COMBINED SHAPES The following shapes are a composite of two shapes in one. Find the total volume of both shapes. Show all work.

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V = prism + pyramid V = BH + 1313 BH V = (64)(5) + 1313 (64)(6) V = 320 +128 V = 448 m 3

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V = cylinder + cone V = r 2 H + 1313 r 2 H V = (4) 2 (3) + 1313 (4) 2 (6) V = 48 + 32 V = 80 ft 3

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