A regular can has a radius of 3 cm and a height of 12.5 cm. The party size can has a radius of 18cm and a height of 37.5cm. If the regular can sells for .35, what should the price of the party size can be if the company wants to base the price on the amount of cola the can will hold?

Guest Jun 12, 2014

#2**+10 **

It looks like we have two cans (cylinders) here. One that is smaller (regular size) and one that is larger (party size) We also know the price of the smaller can. If they want to base the price of the party-sized can proportional to the smaller can, (in other words, you don't get a discount for buying the bigger can) the following should help you find the price of the party-sized can.

These cans probably look something like this:

Let's find the volume of these cans, and then find out how much bigger the party-sized can is, to see how much more it should cost.

Our equation for the volume of a cylinder is **V = (pi)(r ^{2})(h)** ---Volume = (pi)*(radius

The regular can has radius of 3 cm and a height of 12.5 cm, so let's put this in and find it's volume.

**V = (pi)(r ^{2})(h)**

V = (3.14)(3^{2})(12.5)

V = 353.25

Now let's find the volume of the party-sized can:

**V = (pi)(r ^{2})(h)**

V = (3.14)(18^{2})(37.5)

V = 38,151

Now, we can divide the volume of the regular-sized can by the party-sized can to see how much bigger the party-sized can is compared to the regular sized can.

38,151 ÷ 353.25

108

The party-sized can is 108 times as big, so it should be priced 108 times bigger than the regular-sized can.

.35*108 = 37.80

$37.80

NinjaDevo
Jun 12, 2014

#1**+8 **

Assuming that we want the price to be proportional to the volume...

The volume of a cylinder is given by pi*r^2 * h where r is the radius and h is the height

So the volume of the smaller can is given by

pi*(3cm)^2 *(12.5cm)= 353.42 cm^3

And the volume of the larger can is given by

pi*(18cm)^2 *(37.5cm) = 38170.35 cm^3

So...using a ratio...

38170.35/353.42 = x/.35 where x is the price of the larger can = $37.80

Wow!!...that's a pretty pricey can of cola....but...it IS a party, after all!!

CPhill
Jun 12, 2014

#2**+10 **

Best Answer

It looks like we have two cans (cylinders) here. One that is smaller (regular size) and one that is larger (party size) We also know the price of the smaller can. If they want to base the price of the party-sized can proportional to the smaller can, (in other words, you don't get a discount for buying the bigger can) the following should help you find the price of the party-sized can.

These cans probably look something like this:

Let's find the volume of these cans, and then find out how much bigger the party-sized can is, to see how much more it should cost.

Our equation for the volume of a cylinder is **V = (pi)(r ^{2})(h)** ---Volume = (pi)*(radius

The regular can has radius of 3 cm and a height of 12.5 cm, so let's put this in and find it's volume.

**V = (pi)(r ^{2})(h)**

V = (3.14)(3^{2})(12.5)

V = 353.25

Now let's find the volume of the party-sized can:

**V = (pi)(r ^{2})(h)**

V = (3.14)(18^{2})(37.5)

V = 38,151

Now, we can divide the volume of the regular-sized can by the party-sized can to see how much bigger the party-sized can is compared to the regular sized can.

38,151 ÷ 353.25

108

The party-sized can is 108 times as big, so it should be priced 108 times bigger than the regular-sized can.

.35*108 = 37.80

$37.80

NinjaDevo
Jun 12, 2014

#3**+3 **

Nice job ND !!....I don't see any labels on those cans...must be "generic" cola.....

Thumbs Up + Points......

CPhill
Jun 12, 2014

#4**+5 **

I like the abbreviation, CP!

I was actually kind of stumped on this one. I wrote it all out, but my answer really didn't seem that rational, becuause the party can costed so much.

After you posted, I saw we had the same answer so I posted mine quick. Thanks for the verification! :)

NinjaDevo
Jun 12, 2014

#5**0 **

Actually...it didn't seem too reasonable to me, either.....just proves the old adage...."The math doesn't lie".......37 bucks for a can of cola???.....must be REALLY good !!!

CPhill
Jun 12, 2014