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Question 140368: A life saver has a 3cm diameter, a 1cm diamter hole and has 1/2 cm height. Find the volume and total surface area of the life saver. (Just like the candy lifesaver) That is what the pic looks like.
Thankyou Shelly
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A life saver has a 3 cm diameter, a 1 cm diameter hole and has 1/2 cm height. Find the volume and total surface area of the life saver. (Just like the candy lifesaver) That is what the pic looks like.
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The approach to this problem:
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Use the volume (V1) of a cylinder (V=pi*r^2*h) to find the volume if it did not have a hole
Then find the volume (V2)of the material removed to form the hole, also a cylinder. Subtract V2 from V1
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r = 1.5; h = .5
V1 = pi*1.5^2*.5
V1 = 3.5343 cu/cm
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r = .5; h = .5
V2 = pi*.5^2*.5
V2 = .3927 cu/cm
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3.5343 - .3927 = 3.1416 cu/cm is the volume of the life saver
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Surface area approach:
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Find the surface area of a cylinder, ignoring the hole.
Find area of the 2 circles that form the hole. Subtract from the total surface area.
Find the area of the sides of the cylinder forming the hole. Add to above area
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Surface area, ignoring the hole
r = 1.5, d = 3, h = .5
SA = 2(pi*1.5^2) + (pi*3*.5)
SA = 14.1371 + 4.7124
SA = 18.8495 sq/cm
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Area of the 2 circles that form the hole
A = (pi*.5^2) * 2
A = 1.5708 sq/cm
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18.8495 - 1.5708 = 17.2787 sq/cm, surface area not including the inside of the hole
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Find the area of the sides inside the hole: d = 1; h = .5, add to the SA
A = pi*1*.5
A = 1.5708
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Find total surface area:
17.2787 + 1.5708 = 18.8495 sq/cm, total surface area.
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Did this makes sense, by the way what happens to the candy removed from the life saver to form the hole?
I know that with donuts, you can buy donut holes at the bakery here.
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I'm sure, Shelly, these comments, interest you tremendously, hope this helps anyway.
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