Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).

if the soda can is a cylinder, which is most likely, than that means we need to find the height of the cone. The formula for volume of a cylinder is V= пr^2h (look at the pic for clearer formula) and we know the diameter of the soda can is 6, we know the radius is 3 because diameter is a line reaching from one point of the circle to the other. Radius is a line reaching from the center of the circle to the outside as shown in the image. We divide pi (you can put in the calculator 3.14) from 21, then we get 6.688 (if we round up) and then you must look at the formula now

it looks like
6.688=r^2h

that means we must find 3^2
that basically means 3x3 which is 9

then you have to divide that from 6.688

then you get 0.743

that is your height.

now we must find the volume of the cone. The formula for that is

V=пr^2(h/3)

now lets plug in our info

V=(3.14)(9)(0.743/3)

you get 6.999

eudora eudora · Answer 2 · 2019-06-30T14:50:37+02:00

Answer:

Volume of the cone = 7 unit³

Step-by-step explanation:

Soda can has the shape of a cylinder.

Volume of soda can = πr²h

where r = [tex]\frac{6}{2}=3[/tex] units

and volume = 21 unit³

We put the values in the formula to get the value of h.

21 = πr²h

[tex]h=\frac{21}{\pi r^{2} }[/tex]

Now If we fit a cone inside the can, radius of the cone will be equal to the radius of the cylinder and height of the cylinder will be equal to the height of the cone fit inside.

By the formula of volume of cone

Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]

= [tex]\frac{1}{3}\pi r^{2}( \frac{21}{\pi r^{2} })[/tex]

= [tex]\frac{21}{3}=7[/tex] units³

Volume of the cone is 7 unit³