Volume and Angle

[匿名]

2012-10-07 7:42 pm

1. Calculate the capacity of the below prism.

圖片參考：http://imgcld.yimg.com/8/n/HA05298172/o/701210070020313873367150.jpg

2. The volume of the solid right prism ABCDEFGH is 1020 cm^3. The base ABCD of the prism is a trapozium, where AD is parallel to BC. It is given that Angle BAD = 90 degree, AB=12 cm, BC=6 cm and DE= 10cm.
(a) FInd the length of AD.
(b) Find the total surface area of the prism ABCDEFGH

圖片參考：http://imgcld.yimg.com/8/n/HA05298172/o/701210070020313873367161.jpg

3.

圖片參考：http://imgcld.yimg.com/8/n/HA05298172/o/701210070020313873367162.jpg

圖片參考：http://imgcld.yimg.com/8/n/HA05298172/o/701210070020313873367173.jpg

4.

圖片參考：http://imgcld.yimg.com/8/n/HA05298172/o/701210070020313873367174.jpg

5. In a polar coordinate system, the polar coordinates of the points A, B and C are (13, 157degree), (14, 247 degree) and (15, 337 degree) respectively.
(a) Let O be the pole. Are A, O and C collinear? Explain your answer.
(b) Find the area of Triangle ABC.

更新1:

Re: wy 2(b) How to find the area of HECD?

回答 (1)

用戶10012

2012-10-09 2:09 am

✔ 最佳答案

(1) Capacity = [(5.5 + 1.5)(50)/2](20) = (7)(25)(20) = 3500 m^3.
(2)
Volume of prism = [(BC + AD)(AB)/2] x DE
so [(6 + AD)(12)/2] x 10 = 1020
6(6 + AD) = 102
36 + 6 AD = 102
AD = (102 - 36)/6 = 11 cm.
I think you can calculate the total surface area.
(3)
Volume of cone = (1/3)p(48^2)(96) = 73728p cm^3. ( p = pi)
Volume of hemisphere = (2/3)p (60^3) = 144000p cm^3.
(3b)
By Pythagoras thm., height of frustum immersed in milk = sqrt ( 60^2 - 48^2) = 36 cm.
By similar triangle, radius of cone at the milk surface = 48(96 - 36)/96 = 30 cm.
So volume of frustum = 73728p - (1/3)p(30^2)(96 - 36) = 73728p - 18000p = 55728p
so milk remaining in the vessel = 144000p - 55728p = 88272p = 277315 cm^3. = 0.277315 m^3. which is less than 0.3m^3. So disagree.
(4)
Angle ABC = (180 - angle BAE) + (180 - angle BCD) = 72 + 54 = 126.
For the 2 triangles :
angle ABC = angle BCD = 126 (proved)
BC = BC (common)
AB = CD (given)
so the 2 triangles are congruent (SAS)
(5)
Angle AOC = 157 + (360 - 337) = 157 + 23 = 180. So AOC is collinear ( in a straight line).
Angle AOB = (180 - 157) + (247 - 180) = 23 + 67 = 90.
That means BO is perpendicular to AOC.
So area of triangle = (13 + 15)(14)/2 = 28 x 7 = 196.

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