Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can?

Volume of a can:
21 = r² π h
21 = 3² π h
21 = 9 π h
h = 21/ 9π = 7/ 3π
Volume of a cone that fits perfectly inside a can:
V = 1/3 r² π h = 1/3 · 9 π · 7 / 3π = 7
Or you can use: V cone = 1/3 V cylinder ( with the same basis )
V cone = 1/3 * 21 = 7

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RenatoMattice RenatoMattice · Answer 2 · 2019-02-28T10:39:11+01:00

Answer: The volume of a cone that fits perfectly inside the soda can is 7.

Step-by-step explanation:

Since we have given that

Volume of soda can = 21

Diameter of can = 6

As we know the formula for "Volume of cylinder:"

[tex]Volume=\pi r^2h\\\\21=\pi 6^2h\\\\h=\frac{21}{36\pi }\\\\h=\frac{7}{12\pi }[/tex]

Now, we have to find the volume of a cone that fits perfectly inside the soda can.

so, its radius will be 3 cm and height will be [tex]\frac{7}{12\pi }[/tex]

As we know the formula for "Volume of cone":

[tex]Volume=\frac{1}{3}\pi r^h\\\\Volume=\frac{1}{3}\times 6\times 6\times \frac{7}{12\pi}\\\\Volume=7[/tex]

Hence, the volume of a cone that fits perfectly inside the soda can is 7.