Question

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).
Numerical Answers Expected!

Answer 1

Step-by-step explanation:

We know

Volume of a cylinder is $V = \pi r^{2}h$

                                       $V = \pi \left (\frac{D}{2}\right )^{2}h$

where V is volume of the soda can = 36 (given )

          D is diameter = 4 (given )

          h is the height of the soda can  

$V = \pi \left (\frac{D}{2}\right )^{2}h$

$V = \pi \frac{D^{2}}{4}h$

     36 = 3.14 x (16/4) x h  

     36 = 3.14 x 4 x h

    36 = 12.56 x h

∴ 36 / 12.56 = h

 h =  2.87

Now we know that the volume of a cone is given by

$V = \pi\times \frac{D^{2}}{4}\times \frac{h}{3}$

$V = \pi\times \frac{4^{2}}{4}\times \frac{2.87}{3}$

           = 3.14 x 4 x 0.95

          = 11.932

         = 12 (approx.)

Therefore 12 units cube of volume can be easily fitted in a soda can of 36 unit cubes.

Answer 2

The volume of the cone is 12