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

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Presentation transcript:

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

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.

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.

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

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!

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

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

1 3 V = BH B = ½bh B = ½(4)(2.8) B = 5.6 x 5 triangles = 28

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.

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

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

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

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

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.

V = prism + pyramid 1 3 V = BH + BH 1 3 V = (64)(5) + (64)(6) V = 320 + 128 V = 448 m3

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