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valina [46]
3 years ago
9

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). (4 points)
Mathematics
2 answers:
weeeeeb [17]3 years ago
7 0

Answer:

12 unit³

Step-by-step explanation:

Soda can is in the form of a cylinder.

So volume of a soda can = \pi r^{2} h

where volume of can = 36 unit³

and r = \frac{4}{2} units = 2 unit

Now from the given formula

36 = (2)² (h) π

36 = 4 h × π

h = \frac{36}{4}=\frac{9}{\pi }

Now we have to calculate the volume of a cone that fits perfectly inside the can.

Volume of cone =\frac{1}{3}(\pi r^{2}h)

Height of cone = height of can = \frac{9}{\pi } unit

Radius of cone = radius of can = 2 unit

volume of cone = \frac{1}{3}(\pi )(2)^{2} × (\frac{9}{\pi } )

= 3 × 4

= 12 unit³

spin [16.1K]3 years ago
6 0
First we need to find the heigh of the soda can be rearanging the volume formula, . We can make that  We know that V is 36 and radius is half of the diameter, so radius is 2. 

h = 2.87

Now, we can use the height to figure out the volume of a cone. The volume of a cone is 
R is 2 again and h is 2.87


12.56*.96 = 12.0576
So a cone with a volume of 12.0576 is the largest that will fit into the soda can
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