1. Evaluate
(1^2 - 0^2) + (2^2- 1^2) + (3^2- 2^2)+ (4^2- 3^2)+.......+(10^2 - 9^2).
A) 110
B) 123
C) 100
D) 114
E) 125
2. A cylinder with radius 8 and height 17 is rolled long the floor so that it compltes 2 full revolutions. what is the area of the region of the floor that was touched by the cylinder during the roll?
A) 453 pi
B) 434 pi
C) 456 pi
D) 544 pi
E) 478 pi
(pi is 3.14) :)

Question

1. Evaluate
(1^2 - 0^2) + (2^2- 1^2) + (3^2- 2^2)+ (4^2- 3^2)+.......+(10^2 - 9^2).
A) 110
B) 123
C) 100
D) 114
E) 125
2. A cylinder with radius 8 and height 17 is rolled long the floor so that it compltes 2 full revolutions. what is the area of the region of the floor that was touched by the cylinder during the roll?
A) 453 pi
B) 434 pi
C) 456 pi
D) 544 pi
E) 478 pi
 (pi is 3.14) :)

anonymous · Answer

100

anonymous · Answer

1 is a "telescoping sum" meaning that you subtract off all the stuff that came before it.  only term that survive is 10^2=100

anonymous · Answer

for second one circumference of  the circle is 
$$2\pi r=2\pi \times 8=16\pi$$

anonymous · Answer

rolls across twice so you have a rectangle with base 
$$32\pi$$ and height 17 for a total area of 
$$17\times 32\pi=544\pi$$

anonymous · Answer

thank you very much :) for your help