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

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) (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) (Show Source): You can put this solution on YOUR website!
volume for a cylinder is
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

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

cubic yards
Concrete folks sell by the "full yard", so you need 3 yards
RELATED QUESTIONS
Mrs. Moser wants a patio in the shape of a half-circle with a flat side of 16ft. How much (answered by Alan3354,Theo)
find the volume of concrete needed to make a circular patio that has a radius of 24 feet... (answered by rfer)
A 5-inch-thick concrete slab is being poured for a circular patio 20 feet in diameter.... (answered by Fombitz)
Not sure if in correct area for help, but here goes: I have two problems needing help... (answered by josgarithmetic)
A contractor orders 8 cubic yards of premixed cement,all of which is to be used to pour a (answered by josgarithmetic,ikleyn,Theo)
6. A contractor orders 8 cubic yards of premixed cement, all of which is to be used to... (answered by josgarithmetic)
A house is to be built on a rectangular concrete slab measuring 54 feet by 23 feet. If... (answered by scott8148)
A circular fish pond is to be built in one corner of a rectangular shaped patio of... (answered by Theo)
A contractor orders 8 cubic yards of premixed cement, all of which is to be used to pour (answered by checkley77)