Final answer:
The height of cylinder P is twice the height of cylinder Q. The number that multiplies the volume of cylinder Q to be equal to the volume of cylinder P is 2.
Step-by-step explanation:
To find the number that multiplies the volume of cylinder Q to be equal to the volume of cylinder P, we need to consider the relationship between their heights. Given that the height of cylinder P (H) is twice the height of cylinder Q, we can use the formula for the volume of a cylinder to find the answer. The volume of cylinder Q (VQ) is given by VQ = πr²hQ, and the volume of cylinder P (VP) is given by VP = πr²hP. Since the radii (r) of the cylinders are of equal length, we can cancel them out. So, to find the number that multiplies VQ to be equal to VP, we need to compare their heights. Since H = 2hQ, we can substitute this into the equation: VP = πr²H = πr²(2hQ) = 2πr²hQ. Therefore, the number that multiplies VQ to be equal to VP is 2, so the correct answer is B. 2.