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marissa [1.9K]
2 years ago
5

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).
Mathematics
2 answers:
Tomtit [17]2 years ago
5 0
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
Gelneren [198K]2 years ago
5 0

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

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hope this helps :)

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