SOLUTION: If a cylinder has a radius of 3 centimeters and a height of 10 centimeters, calculate its: a. lateral surface area b. total surface area c. Volume

Algebra ->  Surface-area -> SOLUTION: If a cylinder has a radius of 3 centimeters and a height of 10 centimeters, calculate its: a. lateral surface area b. total surface area c. Volume      Log On


   

Question 203267This question is from textbook Mathematics For Technical trades
: If a cylinder has a radius of 3 centimeters and a height of 10 centimeters, calculate its:
a. lateral surface area
b. total surface area
c. Volume This question is from textbook Mathematics For Technical trades

Found 2 solutions by jsmallt9, Earlsdon:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Lateral surface area = (circumference of the base)*height = %282%2Api%2Ar%29h+=+%282%2Api%2A3%2910+=+%286pi%2910+=+60pi square centimeters.
The area of one bases - pi%2Ar%5E2+=+pi%2A3%5E2+=+pi%2A9+=+9pi square centimeters.
The area of both bases = 2*(Area of one base), since they are congruent circles: 2(9pi) = 18pi}}} square centimeters.
Total surface area of a cylinder = Area of the bases + Lateral surface area = 18pi+%2B+60pi+=+78pi square centimeters.
Volume of a cylinder = (area of the base)*height = %289pi%29%2A10+=+90pi cubic centimeters.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
FInd the lateral surface area, the total surface area, and the volume of a cylinder whose radius (r) is 3 cm. and whose height (h) is 10 cm.
a) Lateral surface area is:
A%5Bl%5D+=+2%28pi%29r%2Ah (Area = Circumference times the height) Substitute r = 3 and h = 10.
A%5Bl%5D+=+2%28pi%29%283%29%2810%29
highlight%28A%5Bl%5D+=+60%28pi%29%29 This is the exact answer. For an approximation, substitute pi+=+3.14 to get:
A%5Bl%5D+=+60%283.14%29
highlight_green%28A%5Bl%5D+=+188.4%29sq.cm.
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b) The total surface area of the cylinder is the sum of the lateral surface area (see a) above) and the areas of the top & bottom of the cylinder.
These areas (top & bottom) are the same so you need compute only one and then double it to get both.
Area of the top:
A%5Bt%5D+=+%28pi%29r%5E2 Substitute r = 3.
A%5Bt%5D+=+%28pi%29%283%29%5E2
A%5Bt%5D+=+9%28pi%29 now double this to include the bottom:
A%5Bb%5D+=+2%289%29%28pi%29
highlight%28A%5Bb%5D+=+18%28pi%29%29 For an approximation, substitute pi+=+3.14
A%5Bb%5D+=+%2818%29%283.14%29
highlight_green%28A%5Bb%5D+=+56.52%29sq.cm.
Now add this to the lateral surface area (60%28pi%29) to get:
A%5BT%5D+=+60%28pi%29%2B18%28pi%29
highlight%28A%5BT%5D+=+78%28pi%29%29 Exact answer, or approximately:
highlight_green%28A%5BT%5D+=+244.92%29sq.cm.
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c) The volume of a cylinder is given by:
V+=+%28pi%29%2Ar%5E2%2Ah Substitute r = 3 and h = 10.
V+=+%28pi%29%283%29%5E2%2810%29
highlight%28V+=+90%28pi%29%29 or approximately:
V+=+90%283.14%29
highlight_green%28V+=+282.6%29cu.cm.