Question

Lydia and Adam are buildng a display of soup cans at the market where they work. the display is in the form of a square pyramid, with a base of 81 cans. They will continue making smaller layers until there is one can at the top. Adam is going to the stockroom to get the can they will need.

a. How many layers will be in the display?

b. How many canse will Lydia and Adam use total?

Answer 1

(a). 9 layers

(b). 285

Explanation:

In the question,

The Square Pyramid is needed to be made from the cans.

The base of the pyramid has = 81 cans

So,

Side of the Square = s

So,

`s^(2)=81\\s = 9`

Therefore, the number of cans on one side of the square base = 9 cans

So,

The number of cans will be reducing by 1 in each layer upto the point we are left with only 1 can in the top.

So,

1st layer = 9 cans

2nd layer = 8 cans

3rd layer = 7 cans

4th layer = 6 cans

5th layer = 5 cans

6th layer = 4 cans

7th layer = 3 cans

8th layer = 2 cans

9th layer = 1 can

Number of layers are = 9

(b).

Total number of cans used by Lydia and Adam will be,

Sum of number of cans in all the layers.

`Number\,of\,cans=9^(2)+8^(2)+7^(2)+6^(2)+5^(2)+4^(2)+3^(2)+2^(2)+1^(2)\\Number\,of\,cans=81+64+49+36+25+16+9+4+1\\Number\,of\,cans=285`

Therefore, the number of cans = 285