What is the minimum amount of saran wrap that Tyler will need to cover the pencil holder, to ensure that no sand leaks out?
a) 11.75i * n ^ 2
b) 13.5i * n ^ 2
c) 14.75i * n ^ 2
d) 32.25i * n ^ 2
e) 34i * n ^ 2
It is impossible to determine the amount of saran wrap needed without knowing the dimensions of the pencil holder.
To calculate the minimum amount of saran wrap needed to cover the pencil holder without any sand leakage, we can use the formula for surface area.
The surface area of a cylinder is given by the formula A = 2πrh + πr^2, where r is the radius and h is the height.
Since the pencil holder is a cylinder, let's assume the radius is "n" inches and the height is "2n" inches (as mentioned earlier). Substituting these values into the formula, we get:
A = 2π(n)(2n) + π(n^2)
Simplifying, we get:
A = 4πn^2 + n^2
A = (4π + 1)n^2
So, the minimum amount of saran wrap needed is given by (4π + 1)n^2.
Comparing this with the given options:
a) 11.75i * n^2
b) 13.5i * n^2
c) 14.75i * n^2
d) 32.25i * n^2
e) 34i * n^2
None of the given options match the derived formula (4π + 1)n^2. Therefore, none of the options provided are correct.
To determine the minimum amount of saran wrap needed to cover the pencil holder, we need to consider the area that needs to be covered. In this case, the area can be calculated by multiplying the height (h), the circumference (c), and a small constant factor (k) that accounts for the thickness of the saran wrap:
Area = h * c * k
To find the circumference of the pencil holder, we need to know the radius (r) and use the formula:
Circumference = 2 * π * r
In this question, the radius of the pencil holder is given as n inches.
Therefore, the circumference can be calculated as:
Circumference = 2 * π * n
Now, let's examine the options:
a) 11.75i * n^2
b) 13.5i * n^2
c) 14.75i * n^2
d) 32.25i * n^2
e) 34i * n^2
Since we need to multiply the height (h), circumference (c), and a constant factor (k), we can eliminate the options with only one factor. This eliminates options a) and b):
a) 11.75i * n^2
b) 13.5i * n^2
Now, for the remaining options, we need to compare the constant factors.
c) 14.75i * n^2
d) 32.25i * n^2
e) 34i * n^2
To find the minimum amount of saran wrap needed, the constant factor k should be as small as possible. Comparing the constant factors, we can see that 14.75i is smaller than both 32.25i and 34i.
Therefore, the correct answer is c) 14.75i * n^2