How do I solve this problem?
The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii. If a can with a six-inch radius holds 1½ pints, how many gallons will a similar can with a 24-inch radius hold?

- anonymous

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- dan815

how many pints is a gallon

- anonymous

I don't know, I'll have to google it.

- dan815

okay do that

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## More answers

- dan815

now the volumes of these 2 objects vary as a function of the cubes of their radii

- anonymous

8

- dan815

lets suppose
Volume of Can A = k*r^3
volume of can B = k*R^3
where R= 24 and r=6
we want to see how many of Can A fit in can B so we know hoiw many pints or gallons go in there

- anonymous

Oh, I just feel so stressed and it makes difficult for me to comprehend.

- dan815

okay dont worry we will take this slow

- anonymous

So, what's the very first step in this problem?

- dan815

How do I solve this problem? The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii.

- dan815

The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii.

- dan815

read this sentence

- anonymous

It says you've been typing for a while. Is that an error?

- dan815

let Vol_A be the volume of can with radius r = 6 inches
Vol_A=k*r^3
Vol_A is varying with respect to r^3 so some constant k times r^3

- anonymous

Is there a significance to your typing of the _ symbol?

- dan815

no =.= its just a label for the variable

- dan815

let Vol_B be the volume of can with radius R=24 inches
Vol_B=k*R^3
Vol_B is varying with respect to R^3 so some constant k(notice same constant) times R^3

- dan815

now what we want to know is how many times bigger volume B is than volume A

- dan815

then we will know how many of Vol_A will fit in volume_B

- dan815

|dw:1444022480876:dw|

- anonymous

I don't know.

- dan815

maybe this picture will help

- dan815

if we know how many times bigger the volume of B is than A then we know how many of A will fit in B

- dan815

and each A is 1.5 pints

- anonymous

Ok.

- anonymous

Do we have any numbers concerning B?

- dan815

yes

- dan815

suppose i give u 2 numbers
20 and 3
how many times is 20 bigger than 3, what will ud o

- dan815

do

- anonymous

divided 20 w/ 3

- dan815

right

- anonymous

6.666666666666666666666666666666666666666666666666666666666666666666

- dan815

in the same way u have
VolB= k*R^3
volA=k*r^3
how many A fit in B?

- anonymous

|dw:1444022694437:dw|

- dan815

|dw:1444022725772:dw|

- anonymous

You know, without knowing the numbers, it makes me unsure, but if I had to guess, I'd just divided the two K x r^3

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