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# What is the formula for the volume of a semi-circle

I am trying to get the volume of a semi-circular pool with a diameter of 100 feet and a depth of three feet.

Hi,

Radius (r) = half of diameter = 50 feet

Area (A) of the semi-circular = (1/2)Π r2
The volume = Ah (depth) = (1/2)
Π r2h = (1/2) * 3.14 * 52* 3 = 117.75 (ft3)

If the shape is a sphere,
Volume of a sphere is = 4/3 r3
The depth of half of the sphere is the same as the radius. The volume of half sphere is 2/3 r3

Customer: replied 9 years ago.

If I scan and send the problem, could you give me an idea of which formulas I need to get the total answer. I don't want the answers, just the formulas and how to get to the answer.
Thanks.

Hi,
Sure!
Based on what you said, the shape should be half of the cylinder. In that case, the formulas should be:
volume = Ah (depth) = (1/2)
Π r2h

http://www.mathsteacher.com.au/year9/ch14_measurement/18_cylinder/cylinder.htm

Customer: replied 9 years ago.

1.6 In-Lab & Homework: Working Together for a Solution
For this exercise, you will work in groups. Your lab instructor will divide you into small (3-4 person) groups. Here
is the problem:
Ocean America, an aquarium and theme park in Florida, has decided to build a new show pool for their orca (\killer
whale") show. They want a pool that will surround the audience by the show as much as possible, while providing
plenty of depth for the whales' tricks. There should also be shallow areas where the whales can interact with
the trainers easily. A designer has produced the drawing seen below. Your group's responsibility is to determine
the amount of salt water the new pool will require. The exact amount of water needs to be determined so that
Ocean America can order the correct ltration system. Study the drawing of the pool, which has all the necessary
measurements listed. Notice that the pool is 20 feet deep in most places, with the exception of the two shallow
(lighter) areas, which are 3 feet deep. All measurements on the left and right sides of the pool are exactly the
same. There are no variations in depth except those listed. The bottom is perfectly
at, and meets the walls at a
right angle. Also, the raised portions are completely solid from top to bottom (they are not just platforms) and
they are perfectly semi-circular in shape. The round cut-out in the front is also a perfect semi-circle.
The New Pool
Using your team's knowledge of geometry along with other references (such as the internet or a math textbook),
nd the cubic volume of the pool shown above in cubic feet (ft3), then use that to gure out how many gallons
(g) of water the pool will hold. Your nal solution should list both the cubic volume (ft3) and the volume of water
(g).
Don't worry if the solution (or even the process for nding the solution) isn't immediately obvious... It isn't meant
to be. The real exercise here is to think about the best way to divide the problem into smaller sub-problems and
solve each of those, eventually nding a solution to the problem as a whole. Divide the work among the team as
necessary, but be sure that everyone understands how the nal answer was achieved.

1
Document the process you use to solve the problem. Keep notes of the following:
 How did you break the problem down?
 What formula(s) are needed?
 Where did you nd the necessary formulas?
 What did each team member contribute to the solution?
 The solution to each (simpli ed) part of the problem
 The nal solution
When you have arrived at a solution, each team member should document his/her solution in a plain-text
document (use Notepad or other plain text editor). Be sure to include all the items listed above. Be as descriptive
as necessary to explain the process by which you computed your answer. Name the document \poolVolume.txt"
and save it in your \My Documents" folder. When you nish, submit your solution to the homework portion of
this lab assignment using LabSoft (as described above). If you aren't sure how to submit your solution, be sure
to ask you lab instructor before leaving the lab!
Be sure you have shown your solutions to the lab instructor before you leave the lab!
File to Submit: poolVolume.txt
If you have questions concerning this assignment, be sure to consult with your lab instructor before leaving the lab.