The total number of cannonballs in the stack is 385 and this can be determined by using the arithmetic operations.
Given :
- You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish Army in Sevilla in the year 1842.
- Outside your barracks window is a stack of cannonballs.
The following steps can be used in order to determine the total number of cannonballs:
Step 1 - The first layer of the stack of cannonballs there are a total of [tex](1^2)[/tex] 1 cannonball.
Step 2 - The second layer of the stack of cannonballs there are a total of [tex](2^2)[/tex] 4 cannonballs.
Step 3 - The third layer of the stack of cannonballs there are a total of [tex](3^2)[/tex] 9 cannonballs.
Step 4 - In the last layer that is, the 10th layer of the stack of cannonballs there are a total of [tex](10^2)[/tex] 100 cannonballs.
Step 5 - So, the generalized formula to count the total number of cannonballs in the stack is given below:
[tex]\rm Total \; number \; of \; Cannonballs=\dfrac{n(n+1)(2n+1)}{6}[/tex]
where 'n' is the total number of layers.
Step 6 - Now, substitute the value of 'n' in the above formula.
[tex]\rm Total \; number \; of \; Cannonballs=\dfrac{10(10+1)(2(10)+1)}{6}[/tex]
Total number of Cannonballs = 385
Therefore, the correct option is B).
For more information, refer to the link given below:
https://brainly.com/question/25834626
