![subject](/tpl/images/cats/mat.png)
Mathematics, 25.04.2020 06:47 lucytackett29
The Frustum of a Pyramid. A frustum of a pyramid is the part of the pyramid included between its base and a plane parallel to its base. The figure below shows a square pyramid from which a smaller square pyramid has been cut off.
Each edge of the base of the large pyramid has length a, and its altitude, VO, has length x + h.
48) Write an expression for the volume of the large pyramid.
Each edge of the base of the small pyramid has a length b and its altitude, VP, has length x.
49) Write an expression for its volume.
50) Write an expression for the volume of the frustum (the part shown in green.)
Given that OM and PN are apothems of ABCD and EFGH, it can be shown that â–³VOM ~ â–³VPN.
51) Write experiments for OM and PN in terms of a and b.
52) Why is VO/VP = OM/PN?
53) Rewrite this proportion in terms of x, h, a, and b.
54) Solve your equation for x in terms of h, a, and b.
55) Substitute for x in your answer to exercise 50 and show that the volume of the frustum is â…“ (a2 + ab + b2)h.
There is evidence that the Egyptians used this expression to find the volume of the frustum of a square based pyramid as early as 1890 B. C.*
56) Find the volume of such frustum for which a = 12, b = 3, and h = 8.
The ancient Babylonians used a different expression, ½(a2 + b2)h, to find the volume of the frustum of a square pyramid.
57) Is this expression also correct? Explain.
![ansver](/tpl/images/cats/User.png)
Answers: 2
Another question on Mathematics
![question](/tpl/images/cats/mat.png)
Mathematics, 21.06.2019 18:00
Need on this geometry question. explain how you did it.
Answers: 1
![question](/tpl/images/cats/mat.png)
Mathematics, 21.06.2019 23:50
Which statement explains how you could use coordinate geometry to prove the opposite sides of a quadrilateral are congruent? a. use the slope formula to prove the slopes of the opposite sides are the same. b. use the slope formula to prove the slopes of the opposite sides are opposite reciprocals. c. use the distance formula to prove the lengths of the opposite sides are the same. d. use the distance formula to prove the midpoints of the opposite sides are the same.
Answers: 3
![question](/tpl/images/cats/mat.png)
Mathematics, 22.06.2019 02:00
The plant were you work has a cylindrical oil tank that is 2.5 feet across on the inside and 10 feet high. the depth of the oil in the tank is 2 feet. about how many gallons of oil are in the tank?
Answers: 2
![question](/tpl/images/cats/mat.png)
Mathematics, 22.06.2019 03:00
Write each rational number in the form a/b, where a and b are integers. 1. 5 1/6 2. -12
Answers: 1
You know the right answer?
The Frustum of a Pyramid. A frustum of a pyramid is the part of the pyramid included between its bas...
Questions
![question](/tpl/images/cats/en.png)
![question](/tpl/images/cats/istoriya.png)
![question](/tpl/images/cats/himiya.png)
![question](/tpl/images/cats/himiya.png)
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/geografiya.png)
Geography, 23.04.2020 19:49
![question](/tpl/images/cats/mat.png)
Mathematics, 23.04.2020 19:49
![question](/tpl/images/cats/mat.png)
Mathematics, 23.04.2020 19:49
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/mkx.png)
Arts, 23.04.2020 19:49
![question](/tpl/images/cats/mat.png)
Mathematics, 23.04.2020 19:49
![question](/tpl/images/cats/mat.png)
Mathematics, 23.04.2020 19:49
![question](/tpl/images/cats/mat.png)
Mathematics, 23.04.2020 19:49
![question](/tpl/images/cats/mat.png)
![question](/tpl/images/cats/mat.png)
Mathematics, 23.04.2020 19:49
![question](/tpl/images/cats/himiya.png)
![question](/tpl/images/cats/ekonomika.png)
![question](/tpl/images/cats/mat.png)