Question

A cylindrical mixing tank is to be scaled up to a larger size such that the volume of the larger tank is 91 times that of the smaller one. The ratios of diameter and heights between the two is closest to ______.

A. 5.0
B. 2.0
C. 3.0
D. 4.5
E. 3.5

Answer 1

To find the ratios of diameter and height between the two tanks, you need to calculate their respective dimensions based on the given volume ratio. The answer is closest to 2.0.

Step-by-step explanation:

To find the ratios of diameter and height between the two tanks, we need to calculate their respective dimensions based on the given volume ratio. Let's assume the smaller tank has a radius (r1) and height (h1). The volume of the smaller tank is given by V1 = πr1^2h1. The volume of the larger tank is V2 = 91(πr1^2h1). Since the volume of a cylinder is directly proportional to the product of its base area and height, we can write the ratio of their dimensions as r2^2h2:r1^2h1 = 91. Taking the square root of 91, we get r2h2:r1h1 = sqrt(91).

Now, let's use the information provided . The ratio of the height to radius for a cylinder with h=10r is 10:1. Since we have the ratio r2h2:r1h1 = sqrt(91), we can conclude that the ratio of their heights is 10:1. Therefore, the answer is closest to B. 2.0.