Question

Given a soda can with a volume of 36 and a diameter of 4, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).

Answer 1

First we need to find the heigh of the soda can be rearanging the volume formula, $V = pi * r^2* h$. We can make that $h = \frac{V}{pi * r^2}$ We know that V is 36 and radius is half of the diameter, so radius is 2. $h = \frac{36}{pi * 2^2}$
$h = \frac{36}{pi * 4}$
h = 2.87

Now, we can use the height to figure out the volume of a cone. The volume of a cone is $V = pi * r^2 * \frac{h}{3}$
R is 2 again and h is 2.87
$V = pi * 2^2 * \frac{2.87}{3}$
$pi * 4 * .96$
12.56*.96 = 12.0576
So a cone with a volume of 12.0576 is the largest that will fit into the soda can

Answer 2

For this case what we should do is model the soda can as a cylinder.

We have then:

$V = \pi * r ^ 2 * h$

Where,

r: can radius

h: height of the can

From here, we clear the value of the height:

$h = \frac{V}{\pi * r ^ 2}$

Substituting values we have:

$h = \frac{36}{\pi * 2 ^ 2}\\h = 2.87$

We are now looking for the volume of the cone.

We have then:

$V = (\frac{1}{3}) * (\pi) * (r ^ 2) * (h)$

Substituting values we have:

$V = (1/3) * (\pi) * (2 ^ 2) * (2.87)\\V = 12.02$

Answer:

the volume of a cone that fits perfectly inside the soda can is:

$V = 12.02$