Question

A company makes similar cylindrical containers in two sizes, as shown in the table below.
What is the volume, in cubic inches, of Type 1 containers?

Containers
Radius (in inches)
Volume (in cubic inches)
Type 1
3
?
Type 2
4
113.11

options:

63.62

37.70

47.72

84.83

Answer 1

@psymon please help.

Answer 2

@babyblue123

So the question says that these cylinders are similar. What this means is that if you turn the radii of the two cylinders into a fraction, this should equal the fraction of their heights. So you have two radii, one is 3 and the other 4. So this means that if you put the height of each cylinder into a fraction, it should equal 3/4.

What is given is the radius and the volume of cylinder 2. The formula for a cylinder is
πr^2*h = volume. So basically we are missing the height of this second cylinder, which we can solve for.

\[πr ^{2}h = volume\]
r = 4 so:
\[π(4)^{2}h = 113.11\]
4^2 = 16, so we will divide both sides by 16pi to get:
\[h = \frac{ 113.11 }{ 16π } \approx 2.25\]

Now recall that if we put the height of each cylinder into a fraction, it should = 3/4. So in order to find 3/4 of 2.25, we just multiply 2.25(3/4), which will give us approximately 1.69. This 1.69 is the height of cylinder 1. I won't solve the rest, but this is a major start. I want to make sure this makes sense or if I need to explain further.