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 PYRAMIDSara 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

V = BH13

7.25 – PRACTICENow 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!

V = BH13

V = 13

(64)(3)

V = 64 un3

V = BH13

V = 13

(84)(19)

V = 532 un3

V = BH13

B = ½bh B = ½(4)(2.8)

B = 5.6x 5 triangles = 28

7.26 – CONESWhile 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. Then write a response explaining how to find the volume of a cone based on the formula for the volume of a pyramid.

V = BH13

21

3V r H

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

V = r2H13

V = (4)2(7)13

V = 37.33 yd3

V = r2H13

V = (8)2(9.53)13

V = 203.31 cm3

O

A

tan 40 = 8a

a = 9.53

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

V = prism + pyramid

V = BH + 13

BH

V = (64)(5) + 13

(64)(6)

V = 320 + 128

V = 448 m3

V = cylinder + cone

V = r2H + 13

r2H

V = (4)2(3) + 13

(4)2(6)

V = 48 + 32

V = 80 ft3