Post on 26-Mar-2015
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