Question

Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).

Answer 1

check the picture below

now, if the cone fits perfectly inside the can, that simply means, they both have the same radius "r" and height "h", whatever that might be

Answer 2

Answer: 5 cube unit

Step-by-step explanation:

Since, The volume of a cylinder having radius r and height h

=  $\pi r^2h$

The volume of a cone having radius r and height h

= $\frac{1}{3}\pi r^2h$

Here, the shape of the cone is cylindrical,

And, the diameter of the cylinder = 2 unit,

⇒ The radius of the cylinder = 1 unit,

Let h be the height of the cylinder,

⇒ $\text{ The volume of the cylinder } = \pi (1)^2 h$

According to the question,

$\pi h = 15$

$\implies h = \frac{15}{\pi}$  unit.

Now, the largest cone that can be fit inside the given can must have the same height as the can,

⇒ $\text{ The height of the largest cone} = \frac{15}{\pi}$

Also, the cone must have the same diameter or radius as the can,

⇒ The radius of the largest cone inside the can = 1 unit,

⇒ $\text{ The volume of the largest cone } = \frac{1}{3}\pi (1)^2(\frac{15}{\pi})$

$=\frac{15\pi}{3\pi}$

$=5$ cube unit