You have to go through your x-axis and up or down you y-axis and then determine if the end point are on the right plot form
Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8
Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?
Let's check it out:
Even-numbered lists of odd numbers:
1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .
Amazing ! The sum is always the square of the number of items in the set !
For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.
I slogged through it on my calculator, and it's true.
I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).
Answer:
<h2>
204π units²</h2>
Step-by-step explanation:
The lateral area of the cylinder includes both the side and the ends.
The area of the side can be found by calculating the circumference of the cylinder and multiplying that by the height: A = 2π(6 units )(11 units) = 132π units².
The area of one end of this cylinder can be found by applying the "area of a circle" formula: A = πr². Here, with r = 6 units, A = π(6 units)² = 36π units². Since the cylinder has two ends, the total area of the ends is thus 2(36π units) = 72π units.
The total lateral area of the cylinder is thus 72π units² + 132π units², or 204π units²
