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

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

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**7.5 – What’s 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 1 3 V = BH

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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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1 3 V = BH 1 3 V = (64) (3) V = 64 un3

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1 3 V = BH 1 3 V = (84) (19) V = 532 un3

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1 3 V = BH B = ½bh B = ½(4)(2.8) B = 5.6 x 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**

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. 1 3 V = BH

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

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1 3 V = r2H 1 3 V = (4)2(7) V = 37.33 yd3

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**O A 1 V = r2H 3 1 V = (8)2(9.53) 3 tan 40 = V = 203.31 cm3**

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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 1 3 V = BH + BH 1 3 V = (64)(5) + (64)(6) V = 128 V = m3

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V = cylinder + cone 1 3 V = r2H + r2H 1 3 V = (4)2(3) + (4)2(6) V = 48 32 V = 80 ft3

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