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 can

Answer 1

Answer:

$5cm^{3}$

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, cone an cylinder.

from the formula of cylinder and cone we can see that the volume of a cone is 3 times smaller than that of a cylinder

$volume=\pi r^{2} h$....................cylinder

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

assuming all units in (cm)

Given data.

Volume of cylinder  =  $15cm^{3}$

Diameter d=  $2cm$

Radius r =   $\frac{d}{2}$$= \frac{2}{2} = 1cm$

Height h=  ??

we know that the expression for the volume of a cylinder is

$volume=\pi r^{2} h$

we can substitute our given data to find the height h

$15= 3.142*1^{2}*h\\15= 3.142h$

divide both side by 3.142 we have

$h= \frac{15}{3.142}\\ h= 4.77cm$

We can now use this height$4.77cm$ and radius $1cm$ to find the equivalent  volume of a cone.

the expression for the volume of a cone is

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

substituting our data into the expression  we have

$volume= \frac{3.142*1^{2*} 4.77}{3} \\volume= \frac{15}{3} \\voulume = 5cm^{3}$