Question 148492
Well it is a cola in a bottle so we need to find the {{{"radius"}}} (very important) that we'll used in the calculations. Next, we'll assume it's a cola in can with cylindrical shape because ther'es no formula for finding area & volume for "curvature" bottle (2 curves? 3 curves?, we don't know)
1)For the {{{Volume=pi*r^2h}}} where the height will be the lengths given.
Let's follow the following designation,
{{{V[1]=pi(r[1])^2(h[1])}}} -------------- smaller size
{{{V[2]=pi(r[2])^2(h[2])}}} -------------- bigger size
Since {{{V[2]}}} is given, we'll solve this first,
{{{15liters=pi(r[2])^2 (15 centimeters)}}}
We have to remember, {{{1Liter=1000 cm^3}}}
{{{(r[2])^2= (1500cm^3)/(pi*15cm)}}} {{{r[2]=sqrt(32)}}}
{{{r[2]= 6 cm}}} -----------> if you want exact =5.6 cm
And remember {{{r[1]=r[2]}}} because they're similar right as stated.
So for {{{V[1]=pi(56)^2(12cm)}}} {{{V[1]=1182 cm^3}}}= 1.18 Liters ---> smaller
2) for the Area of the bigger cola, we need to get the {{{Area of the ends+ Area of the cylindrical side}}}= {{{A[2]=2pi(r[2])^2 + 2pi(r[2])(h[2])}}}
{{{A[2]=2pi(56)^2 + 2pi(56)(15)}}}={{{197+528}}}
{{{A[2]=725 cm^2}}} ------------> bigger

<pre><font size=4=indigo><b>Thank you,
Jojo</pre>