Answer: cos(Θ) = (√15) / 4
Explanation:
The question states:
1) sin(Θ) = 1/4
2) 0 < Θ < π / 2
3) find cos(Θ)
This is how you solve it.
1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).

2) From which you can find:

3) Replace sin(α) with 1/4
=>

=>

4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:
cos(Θ) =

.
And that is the answer.
The answer is C because it shows you
givens
pi = 3.14
r = 2
h = 4
Formula
v = pi r^2 h
Sub and Solve
V = 3.14 * 2^2 * 4
V = 3.14 * 4 * 4
V = 3.14 * 16
V = 50.24