Question

Two cylindrical cans with the same height have radii of 2 and 3 inches, respectively. The capacity of the smaller can is 0.5 gallon. What is the capacity of the larger can, in gallons?

Answer 1

The capacity of the larger can, when compared to the smaller can, is 1.125 gallons.

Step-by-step explanation:

To find the capacity of the larger can in gallons, we need to compare the volumes of the two cans. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Let's calculate the volume of the smaller can first:

Vsmaller = π(2 in)²h = 4πh

Since the capacity of the smaller can is 0.5 gallon, we can set up the following proportion: Vsmaller / Vlarger = 0.5 / ?

By substituting the values, we get: 4πh / Vlarger = 0.5 / ?

Now, let's calculate the volume of the larger can:

Vlarger = π(3 in)²h = 9πh

We can substitute this value into the proportion: 4πh / (9πh) = 0.5 / ?

Simplifying the equation, we get: 4/9 = 0.5 / ?

Cross-multiplying and solving for ?, we find: ? = (9 * 0.5) / 4

? = 4.5 / 4 = 1.125

Therefore, the capacity of the larger can is 1.125 gallons.