Question

The information below is used in the last 2 questions:

The two cylinders shown below contain oatmeal. The small cylinder has a radius of 3 inches and a height of 10 inches. The large cylinder has a radius of 6 inches and a height of 10 inches (the radius is doubled). If the small container of oatmeal costs $3, what is a fair price for the large container?

$9

$12

$6

$24

Answer 1

The fair price for the large container is $12

Explanation:

In this question, we are tasked with calculating what would be the fair price for the large cylinder given the price for the small cylinder.

To calculate this, what we need to do firstly is to estimate the the volumes of both cylinders.

Mathematically, the volume of a cylinder can be calculated using the formula; V = π ×
`r^(2)`×h

For the small cylinder, r = 3 inches and h = 10 inches

Thus
`V_(s)` = π ×
`3^(2)`× 10 = 90π
`inches^(3)`

For the large cylinder, r = 6 inches and h = 10 inches

Thus
`V_(l)` = π ×
`6^(2)`× 10 = 360π
`inches^(3)`

Now let us find the ratio of their volumes = 360π/90π = 4

Since the ratio of their volumes is 4, it can be fair to say that the large cylinder should cost 4 times the price of the small cylinder = 4 × $3 = $12