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two Eng. Maths. question?(20點)
發問:
只要步驟1. A picture frame is in the shape of a rectangle. All the measurements are shown in the figure and are correct to the nearest cm. Find the maximum and minimum areas of the picture frame. 86cm -----------------------｜ _________ ｜｜ ｜ 70cm ｜｜｜ ｜46cm ｜｜56cm｜... 顯示更多 只要步驟 1. A picture frame is in the shape of a rectangle. All the measurements are shown in the figure and are correct to the nearest cm. Find the maximum and minimum areas of the picture frame. 86cm ----------------------- ｜ _________ ｜ ｜ ｜ 70cm ｜｜ ｜ ｜46cm ｜｜56cm ｜ ｜_______｜｜ ｜___________ ｜ answer: maximum area=2176 cm2 , minimum area=1920 cm2 2. The figure shows an open rectangular glass tank of uniform thickness. The external length, width and height are measured to be 320mm, 228mm and 200mm respectively. The thickness of the glass is meaured to be 8mm. All the measurements are correct to the nearest mm. Find the maximum and minimum capacities of the tank. (Give your answers ccorrect to the nearest mm3. answer: maximum capacity=12588280 mm3 , minimum capacity=12162164 mm3
最佳解答:
In your questions, all the measurements seemed to be accurate. Why there are maximum and minimum values? Is there anything information missing? Such as tolerance. e.g. the length for the open rectangular glass tank in Q.2 is (320 +/- 1)mm Or is there any implication for the phrase "correct to the nearest mm"? From the information given, I can only give the following answers : 1. The area of the picture frame = [(86)(56) - (70)(46)] cm^2 = (4816 - 3220) cm^2 = 1596 cm^2 2. The capacity of the open rectangular glass tank = {[320 - 2(8)][228 - 2(8)][200 - (8)]} mm^3 __(Since the tank is open, only one thickness of the glass should be __subtracted from the height.) = [(304)(212)(192)] mm^3 = 12374016 mm^3 If you find out any extra information, please tell me and I shall give you the correct answers as soon as possible. 2009-03-14 11:01:34 補充： I have a guess on the phrase "correct to the nearest mm". That is to give a tolerance of "+/- 0.5 mm" to the measurements. So, I now provide my corrected answers as follows : 2009-03-14 11:02:10 補充： 1. The maximum area of the picture frame = [(86.5)(56.5) - (69.5)(45.5)] cm^2 = (4887.25 - 3162.25) cm^2 = 1725 cm^2 2009-03-14 11:02:29 補充： The minimum area of the picture frame = [(85.5)(55.5) - (70.5)(46.5)] cm^2 = (4745.25 - 3278.25) cm^2 = 1467 cm^2 (For the wrong answers of Q.1, I think it is due to the wrong information given.) 2009-03-14 11:02:45 補充： 2. The maximum capacity of the open rectangular glass tank = {[320.5 - 2(7.5)][228.5 - 2(7.5)][200.5 - (7.5)]} mm^3 = [(305.5)(213.5)(193)] mm^3 = 12588280 mm^3 (correct to the nearest mm^3) 2009-03-14 11:02:58 補充： The minimum capacity of the open rectangular glass tank = {[319.5 - 2(8.5)][227.5 - 2(8.5)][199.5 - (8.5)]} mm^3 = [(302.5)(210.5)(191)] mm^3 = 12162164 mm^3 (correct to the nearest mm^3)
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