SOLUTION: A patio in the shape of a half circle and is 4 inches thick is being built. The radius is 12 feet. To the nearest cubic yard, how much concrete will be needed? How did they come

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A patio in the shape of a half circle and is 4 inches thick is being built. The radius is 12 feet. To the nearest cubic yard, how much concrete will be needed? How did they come       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 150874This question is from textbook number power
: A patio in the shape of a half circle and is 4 inches thick is being built. The radius is 12 feet.
To the nearest cubic yard, how much concrete will be needed?
How did they come up with 3 cubic yds of concrete?
Could you please explain this for me, I am so lost. I am so grateful for any help.
Thank-You This question is from textbook number power

Found 2 solutions by stanbon, vleith:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A patio in the shape of a half circle and is 4 inches thick is being built. The radius is 12 feet.
To the nearest cubic yard, how much concrete will be needed?
How did they come up with 3 cubic yds of concrete?
-------------------------
The half circle has a surface area of (1/2)(pi)r^2
Your radius is 12 feet so the surface is (1/2)pi^12^2 = 226.19 sq. ft.
-------------
The depth of the patio is 4 incles or (1/3) ft
--------------
So the volume of the patio is (1/3)(226.19) = 75.4 cu. ft.
--------------
A cubic yard of cuncrete is 3 ft x 3 ft x 3ft = 27 cu. ft.
-----------------------------
Dividing 75.4 cu. ft by 27 cu. ft you get 2.79 cu. yd of concrete.
====================
Cheers,
Stan H.

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
volume for a cylinder is V=+pi%2Ar%5E2%2Ah
Think of a cylinder as a whole bunch of circles stacked on top of each other. So the Volume is just the area of each thin circle times the height of the stack.
In this case, the shape is only a half circle. So the formula we need is
V+=+%28%28pi%2Ar%5E2%29%2F2%29%2Ah
Our radius is 12 feet. Our height is 1/3 foot. And the answer is in cubic yards.
So we will need to convert everything to yards
12 feet = 4 yards
4 inches = 1/9 yard
V+=+%28%28pi%2A4%5E2%29%2F2%29%2A%281%2F9%29
V+=+%28%28pi%2A16%29%2F2%29%2A%281%2F9%29
V+=+%28%28pi%2A16%29%2F18%29
V+=+2.79 cubic yards
Concrete folks sell by the "full yard", so you need 3 yards