ingot of aluminum: volume, weight and area.

jacob_1988

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I have three questions regarding the image above, could someone please help me to understand the problem solving of these please? So I may be able to answer them correctly?

The diagram above shows an ingot of aluminum. The end is in the shape of a Trapezium.

Question: Find the volume of the ingot?
My answer: 1/2(7.4 + 15)x8 = 90. 90 x length = 2250cm2
1/2(a+b)xh.

Question: 1 cm3 of aluminum weighs 2.7g. How heavy is the ingot?
My answer: 6075g.

Question: Someone has to paint one of the ingots black for a scientific experiment. What is the area to be covered?

I don't know where to start on this one... please help :(
 
View attachment 3713

I have three questions regarding the image above, could someone please help me to understand the problem solving of these please? So I may be able to answer them correctly?

The diagram above shows an ingot of aluminum. The end is in the shape of a Trapezium.

Question: Find the volume of the ingot?
My answer: 1/2(7.4 + 15)x8 = 90. 90 x length = 2250cm2 Volume must be in cm3
1/2(a+b)xh.

Question: 1 cm3 of aluminum weighs 2.7g. How heavy is the ingot?
My answer: 6075g.

Question: Someone has to paint one of the ingots black for a scientific experiment. What is the area to be covered?

Total surface area = 2 small trapezoids + one rectangle at the bottom + one rectangle at the top + 2 rectangles on the sides

You know how to calculate areas of trapezoids and rectangles - correct!!

I don't know where to start on this one... please help :(
.
 
:Total surface area = 2 small trapezoids + one rectangle at the bottom + one rectangle at the top + 2 rectangles on the sides

2x1/2(22.5)x8+8x15+8x7.5+2(6x25)=660.

Breakdown of numbers.
(2 small trapezoids) - 2 x 0.5 (22.5) x 8 = 180.
(plus one rectangle at the bottom plus one rectangle at the top) + 8 x 15 + 8x 7.5 = 180.
(plus 2 rectangles on the sides) + 2 (6x25) = 300.

Is that all correct? If so the result should be 660?
 
You're showing one of lengths as 6: is that correct?! Or should it be 8?

(plus 2 rectangles on the sides) + 2 (8x25) = 400.
=760?

Why do you show 8 * 7.5 as one of the areas?

Bottom rectangle = 8x15, Top rectangle = 8x7.5? Height 8cm x width 7.5?
 
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Is the front trapezium 7.5 by 6 by 15 by 8 as you show?


h.JPG

So one trapezium = (7.5 by 6) and the other one = (15 by 8)
trapezium 1/2 a+b x h???
A+B (the bases... top base 7.5 bottom base 15)?

0.5(7.5+15) x 8 = 90
0.5(7.5+15) x 6 = 67.5
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Jacob, you're giving me a headache :razz:

As long as I don't give you a nervous breakdown!!
 
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I presume it's the same?

The red question mark indicates that you're not sure. Please check with your instructor, to get the actual dimensions.

Also, WHY would you label your new diagram with an 8, if you're trying to say that measurement is the SAME as the one in your first diagram (which is labeled 6)?

This thread is very confusing. :sad:
 
The red question mark indicates that you're not sure. Please check with your instructor, to get the actual dimensions.

Also, WHY would you label your new diagram with an 8, if you're trying to say that measurement is the SAME as the one in your first diagram (which is labeled 6)?

This thread is very confusing. :sad:

I have the following diagram on my assignment the front is a trapezium, I'm trying to solve the area... but the front trapezium has two numbers on each side (an eight and a six), I'm very confused as to which one I should use for height?

Moreover; I will get in touch with my teacher and ask him, so everybody please bear with me to I find the correct measurements?
5ea50c1fb5ae601044417955f1dcf747.png
 
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I've been told... to find the height you need to treat it [Trapezium] as a triangle with the side being the hypotenuse and knowing the other side you use pythagorus to determine the height.

How do I calculate the hypotenuse(s) together... i.e. if one is 45 and the other is 120 - how do
I come to the correct number?


Side A:
h2 = 7.52 + 62 = 56.25 + 36
h = 56.25 + 36 = 2025
h = √2025 = 45

Side B:
h2 = 82 + 152 = 64 + 225
h = 64 + 225 = 14400
h = √14400 = 120
 
Sorry for the delay.

67.5 x 25 = 1687.5cm3
(0.5(22.5)x6 = 67.5. 67.5 x 25 = 1687.5).

two end area = 135.area of top 7.5 x 25 = 187.5.

area of base 15 x 25 = 375.

two sides have area 8 x 25 = 200.

= 897.5cm3.
 
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