How do you find the area of this?  I had to do an experiment where you take a styrofoam cup and poke a flashlight through the bottom of it, then shine the light onto a wall from different distances and measure the diameter. I have to calculate the area. It it just pi*r^2? That's what I did, but then I've seen someone else use 4*pi*r^2 and that confused me. I want to make sure I done it right.

College Physics
10th Edition
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Introduction
Section: Chapter Questions
Problem 43P: A high fountain of water is located at the center of a circular pool as shown in Figure P1.47. Not...
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How do you find the area of this? 
I had to do an experiment where you take a styrofoam cup and poke a flashlight through the bottom of it, then shine the light onto a wall from different distances and measure the diameter. I have to calculate the area. It it just pi*r^2? That's what I did, but then I've seen someone else use 4*pi*r^2 and that confused me. I want to make sure I done it right. 

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So in this instance am I doing it correctly or do I need to use the other formula instead? 

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