Final answer:
Given the formula for joint variation, p as the cube root of q and the cube of r, we determined the constant of proportionality (k) using the initial values. We then used this constant to calculate the new value of p, which resulted in p = 13.5, a value not listed in the given choices.
Step-by-step explanation:
The student asked about a situation where p varies jointly as the cube root of q and the cube of r. We're given that p = 1 when q = 4 and r = 2, and we need to find the new value of p when q = 11 and r = 6.
First, we need to establish the joint variation equation. Since p varies jointly as the cube root of q and the cube of r, we can write the equation as:
p = k ∙ ∛q ∙ r^3, where k is the constant of proportionality. Using the given values, we can find k using 1 = k ∙ ∛4 ∙ 2^3. This simplifies to 1 = k ∙ 2 ∙ 8 or k = 1/16.
Now, we can find the new value of p using q = 11 and r = 6 by substituting these values and our constant k into the equation:
p = (1/16) ∙ ∛11 ∙ 6^3. After calculating, this gives us p = (1/16) ∙ ∛11 ∙ 216, which simplifies to p = 13.5. However, since this is not one of the choices provided, it appears there may be a typo in the question. If the given choices are the only options, either there is a mistake in the question or calculation process.