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

the volume of the cone will be 1/3 of the can .

that is 5

Answer 2

5 cubic units.

Explanation:

We have been given that a can soda can has a volume of 15 cubic units and a diameter of 2.

First of all let us find the height of cylinder using volume of cylinder formula.

`\text{Volume of cylinder}=\pi r^2 h`, where,

r = radius of cylinder,

h = Height of cylinder.

Now let us divide our diameter by 2 to get the radius of cylinder.

`\text{radius of cylinder}=(2)/(2)=1`

Let us substitute our given values in volume of cylinder formula to get the height of cylinder.

`15=\pi*1^2*h`

`15=\pi*h`

`(15)/(\pi)=(\pi*h)/(\pi)`

`(15)/(\pi)=h`

Now we will use volume of cone formula to find the volume of our given cone inscribed inside cylinder.

`\text{Volume of cone}=(1)/(3)\pi*r^2h`

Since the height and radius of the largest cone that can fit inside the can will be equal to height and radius of can, so we will substitute
`(15)/(\pi)=h` and
`r=1` in the volume formula of cone.

`\text{Volume of cone}=(1)/(3)\pi*1^2*(15)/(\pi)`

`\text{Volume of cone}=(1)/(3)*1*15`

`\text{Volume of cone}=5`

Therefore, volume of our given cone will be 5 cubic units.