Math in Daily Life: Canned Goods

Geometry Level 2

You're ordering canned foods to send to charity. You buy:

  1. 100 cans of one-inch radius and one-inch height,
  2. 81 cans of two-inch radius and two-inch height,
  3. 64 cans of three-inch radius and three-inch height,
  4. 49 cans of four-inch radius and four-inch height,
  5. 36 cans of five-inch radius and five-inch height,
  6. 25 cans of six-inch radius and six-inch height,
  7. 16 cans of seven-inch radius and seven-inch height,
  8. 9 cans of eight-inch radius and eight-inch height,
  9. 4 cans of nine-inch radius and nine-inch height, and finally
  10. 1 can of ten-inch radius and ten-inch height.

But, I also need to keep some of the cans for myself. I can't just give all my food to charity! I need to keep 1748π for myself.

If the total volume of all cans added together equals xπ, what is the value of x-1748?


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