Sphere Surface Area and Volume Exercise - October 25, 2011 It may come as a surprise to find that a sphere’s surface area-to-volume ratio does not remain constant as the size of the sphere changes. Today, we will investigate this trend as sphere radius is varied using two different approaches: 1) Direct measurement and comparison of different size spheres. 2) Excel plots of parameters with varying sphere radius. Here are the formulas for sphere surface area and volume, where r is radius: SA/V Activity Part 1: Step 1: Record the volume of the plastic container in cm3. Volume:_____cm3 Step 2: Fill the container with as many tennis balls as you can without any of the tennis balls sticking out of the top of the box. Measure the diameter of one of the tennis Calculate the surface area and volume of the tennis ball and multiply by the total number of tennis balls in the container. Calculate the SA:V by dividing the total surface area by the total volume. Calculate the volume by subtracting the total volume from the volume of the “wasted” plastic container that was calculated in step 1. Diameter:_____cm Surface Area:_____cm2 Volume:_____cm3 # of Tennis Balls:_____ Total Surface Area:_____cm2 Total Volume:_____cm3
Sphere Surface Area and Volume Exercise - October 25, 2011 It may come as a surprise to find that a sphere’s surface area-to-volume ratio does not remain constant as the size of the sphere changes. Today, we will investigate this trend as sphere radius is varied using two different approaches: 1) Direct measurement and comparison of different size spheres. 2) Excel plots of parameters with varying sphere radius. Here are the formulas for sphere surface area and volume, where r is radius: SA/V Activity Part 1: Step 1: Record the volume of the plastic container in cm3. Volume:_____cm3 Step 2: Fill the container with as many tennis balls as you can without any of the tennis balls sticking out of the top of the box. Measure the diameter of one of the tennis Calculate the surface area and volume of the tennis ball and multiply by the total number of tennis balls in the container. Calculate the SA:V by dividing the total surface area by the total volume. Calculate the “wasted” volume by subtracting the total volume from the volume of the plastic container that was calculated in step 1. Diameter:_____cm Surface Area:_____cm2 Volume:_____cm3 # of Tennis Balls:_____ Total Surface Area:_____cm2 Total Volume:_____cm3
sa-to-vol.docx