Final answer:
The volume of cylinder P is twice the volume of cylinder Q because the height of cylinder P is twice that of cylinder Q, while the radii are equal.
Step-by-step explanation:
The question is asking how many times larger the volume of cylinder P is as compared to cylinder Q, given that cylinder P has twice the height of cylinder Q but both have equal radii. To find the volume of a cylinder, we use the formula V = πr²h, where V is the volume, π is the constant pi (approximately 3.14159), r is the radius, and h is the height of the cylinder.
Since both cylinders have equal radii, the ratio of their volumes will only depend on the ratio of their heights. If we let the height of cylinder Q be h, then the height of cylinder P is 2h. Using the volume formula:
Volume of cylinder P, VP = πr²(2h) = 2πr²h.
By dividing the volume of P by the volume of Q, we get:
VP / VQ = (2πr²h) / (πr²h) = 2.
Therefore, the volume of cylinder P is twice the volume of cylinder Q.