SOLUTION: How many square inches of metal are needed to make a soup can that is 2 2/3 in. in diameter and 4 in. high? The answer is (128 pi)/9 in. I'm not sure how to get to that answer. Tha

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Question 955610: How many square inches of metal are needed to make a soup can that is 2 2/3 in. in diameter and 4 in. high? The answer is (128 pi)/9 in. I'm not sure how to get to that answer. Thank you!!!!
Found 4 solutions by Zucchini, josgarithmetic, lwsshak3, MathTherapy:
Answer by Zucchini(70)   (Show Source): You can put this solution on YOUR website!
the first thing that should be considered, is that we are thinking f a cylinder. This problem can be done in several steps. The first step that I would take is, find the circumference of the circle. The formula for the circumference of the circle is C = d · Pi, where d is the diameter. I would first convert 2 2/3 into an improper fraction, so it will be 8/3.
(pi)(8/3)
8/3 pi.
Now, we can multiply that by 4 to get the area of the rectangle part of the cylinder.
(8/3 pi)(4)
32/3 pi
Now we will find he area of the two circles: (pi · R^2)
(pi)((4/3)^2)
16/9 pi
To get the area of both of the corcles, we can just multiply that by 2. So, 32/9 pi.
Now, we just add 32/3 pi and 32/9 pi. In order to do this, we need common denominators. When you get them and add the two numbers, you get 128/9 pi
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Imagine a circle of diameter inches. One of them is at the top of the can, and another is at the bottom of the can. These two circles have a combined area.

The circumference of either circle is just one linear length value. Extending the circumference upward by 4 inches creates an area for the cylindrical side of the can.

Now can you form the expression for the entire surface area for this can?



Simplify that.
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
How many square inches of metal are needed to make a soup can that is 2 2/3 in. in diameter and 4 in. high? The answer is (128 pi)/9 in. I'm not sure how to get to that answer.
***
diameter=2 2/3 in=8/3 in
radius=8/6=4/3 in
area of 2 ends=2*πr^2=2*π(4/3)^2=2π(16/9)=32π/9
area between ends=2πr*height=2π(4/3)*4=32π/3=96π/9
Total area=32π/9+96π/9=128π/9
How many square inches of metal are needed to make the soup can? 128π/9
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
How many square inches of metal are needed to make a soup can that is 2 2/3 in. in diameter and 4 in. high? The answer is (128 pi)/9 in. I'm not sure how to get to that answer. Thank you!!!!
Radius of can: ____________

Area of top and bottom: _________________



Lateral area of right circular cylinder (can): __________________



Area of metal needed: , or , or  sq inches. 

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