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). …

Question

asked Jul 24, 2019 210k views

2 Answers

Mariya Steksova · Answer 1 · 2019-07-28T08:31:18+0000

Explanation:

We know

Volume of a cylinder is
$V = \pi r^(2)h$

$V = \pi \left ((D)/(2)\right )^(2)h$

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

D is diameter = 4 (given )

h is the height of the soda can

$V = \pi \left ((D)/(2)\right )^(2)h$

$V = \pi (D^(2))/(4)h$

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

$V = \pi*  (D^(2))/(4)* (h)/(3)$

$V = \pi*  (4^(2))/(4)* (2.87)/(3)$

= 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.