Jake has two similar cylindrical pipes. The radius of the first cylindrical pipe is 5 cm. The circumference of the second cylindrical pipe is 20π cm.

The volume of the second cylindrical pipe is how many times greater than the volume of the first cylindrical pipe?

A.3
B.4
C.5
D.8

since C=2pi*r, the radius of the 2nd pipe is 20π/2π = 10

so, the 2nd pipe has radius twice the 1st pipe.

If linear dimensions scale by n,
area scales by n^2
volume scales by n^3

So, now you have what you need.

To find the volume of a cylinder, we use the formula V = πr^2h, where V is the volume, r is the radius, and h is the height of the cylinder.

First, let's determine the radius and height of the second cylindrical pipe.
We are given the circumference of the second cylindrical pipe, which is 20π cm. The formula for the circumference of a cylinder is C = 2πr, where C is the circumference and r is the radius.
Since the circumference is given as 20π cm, we can set up the equation 20π = 2πr and solve for r.
Dividing both sides of the equation by 2π, we get r = 10 cm.

Now, let's calculate the volume of the first cylindrical pipe.
The radius of the first cylindrical pipe is given as 5 cm. Let's assume the height of both pipes is the same for simplicity, and we can compare the volumes later.

Using the formula V = πr^2h, for the first cylindrical pipe, we have V1 = π(5 cm)^2h.
Simplifying this expression, we get V1 = 25πh.

Now, let's calculate the volume of the second cylindrical pipe.
The radius of the second cylindrical pipe is 10 cm, and assuming the same height as the first pipe, we have V2 = π(10 cm)^2h.
Simplifying this expression, we get V2 = 100πh.

To compare the volumes, we divide the volume of the second cylindrical pipe by the volume of the first cylindrical pipe:
V2/V1 = (100πh) / (25πh)
Canceling out the common factor of πh on both sides, we get V2/V1 = 100/25
Simplifying the fraction, we find V2/V1 = 4.

Therefore, the volume of the second cylindrical pipe is 4 times greater than the volume of the first cylindrical pipe.

The correct answer choice is B. 4.